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Gongyo, Shinya. "The Gribov problem beyond Landau gauge Yang-Mills theory." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199098.
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Maas, Axel Torsten. "The high-temperature phase of Yang-Mills theory in Landau gauge." Phd thesis, [S.l. : s.n.], 2004. http://elib.tu-darmstadt.de/diss/000504.
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Grosse, Harald, Thomas Krajewski, Raimar Wulkenhaar, and grosse@doppler thp univie ac at. "Renormalization of Noncommutative Yang-Mills Theories: A Simple Example." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi914.ps.
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Slater, Matthew J. "Instanton effects in supersymmetric SU(N) gauge theories." Thesis, Durham University, 1998. http://etheses.dur.ac.uk/4812/.
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We investigate nonperturbative effects due to instantons in N = 2 supersymmetric SU(N) Yang-Mills models, with the aim of testing the exact results predicted for these models. In two separate semiclassical calculations we obtain the one-instanton contribution to the Higgs condensate u(_3) = (TrA(^3)) and to the prepotential F. Comparing our results with the exact predictions, we find complete agreement except when the number of flavours of fundamental matter hypermultiplets, N(_f), takes certain values. The source of the u(_3) discrepancy is an ambiguity in the parameterization of the hyperelliptic curves from which the exact predictions are derived when N(_f) ≥ N. This ambiguity can easily be fixed using the results of instanton calculations. The discrepancy associated with T appears in the finite N(_f) = 2N models. For these models we are unable to modify the curves to agree with the instanton calculations when N > 3. Our one-instanton calculation of the prepotential is facilitated by a multi-instanton calculus which we construct, starting from the general solution of Atiyah, Drinfeld, Hitchin and Manin. Our calculus comprises: (i) the super-multi-instanton background, (ii) the su persymmetric multi-instanton action and (iii) the supersymmetric semiclassical collective coordinate measure. Our calculus has application to supersymmetric Yang-Mills theory with gauge group U(N) or SU(_N). We employ our instanton calculus to derive results at arbitrary k-instanton levels. In N =2 supersymmetric SU(N) Yang-Mills theory, we derive a closed form expression for the A;-instanton contribution to the prepotential. This amounts to a solution, in quadratures, of the low-energy physics of the theory, obtained from first principles. In supersymmetric SU(2) Yang-Mills theory, we use our calculus to investigate multi-instanton contributions to higher-derivative terms in the Wilsonian effective action. Using a scaling argument, based on general properties of the SU(2) k-instanton action and measure, we show that in the finite, massless N = 2 and N = 4 models, all k-instanton contributions to the next-to- leading higher-derivative terms vanish. This confirms a nonperturbative nonrenormalization theorem due to Dine and Seiberg.
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Trocsanyi, Zoltan L. "Three-loop renormalization of Yang-Mills theory in background field gauge." Diss., Virginia Tech, 1990. http://hdl.handle.net/10919/39413.
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Mariani, Alessandro. "Finite-group Yang-Mills lattice gauge theories in the Hamiltonian formalism." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21183/.
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Nuovi sviluppi nel campo nelle tecniche sperimentali potrebbero presto permettere la realizzazione di simulatori quantistici, ovvero di sistemi quantomeccanici realizzabili sperimentalmente che descrivano una specifica Hamiltoniana di nostra scelta. Una volta costruito il sistema, si possono effettuare esperimenti per studiare il comportamento della teoria descritta dall'Hamiltoniana scelta. Un'interessante applicazione riguarda le teorie di gauge non-Abeliane come la Cromodinamica Quantistica, per le quali si hanno un certo numero di problemi irrisolti, in particolare nella regione a potenziale chimico finito. La principale sfida teorica per la realizzazione di un simulatore quantistico è quella di rendere lo spazio di Hilbert della teoria di gauge finito-dimensionale. Infatti in un esperimento si possono controllare realisticamente solo alcuni gradi di libertà del sistema quantistico, e certamente solo un numero finito. Seguendo alcune linee già tracciate in letteratura, nel presente lavoro ottieniamo uno spazio di Hilbert finito-dimensionale sostituendo il gruppo di gauge - un gruppo di Lie - con un gruppo finito, ad esempio uno dei suoi sottogruppi. Dopo una rassegna della teoria di Yang-Mills nel continuo e su reticolo, ne diamo la formulazione Hamiltoniana enfatizzando l'introduzione del potenziale chimico. A seguire, introduciamo le teorie basate su un qualsiasi gruppo di gauge finito, e proponiamo una soluzione ad un problema irrisolto di tali teorie, cioè la determinazione degli autovalori della densità di energia elettrica. Effettuiamo inoltre alcuni calcoli analitici della tensione di stringa in teorie con gruppo di gauge finito, e risolveremo esattamente alcune di esse in un caso semplificato. A finire, studieremo il comportamento dello stato fondamentale di tali teorie tramite un metodo variazionale, e offriremo alcune considerazioni conclusive.
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陶福臻 and Fook-tsun To. "Soliton solutions to gravitational field and Yang-Mills gauge field." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31233910.
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To, Fook-tsun. "Soliton solutions to gravitational field and Yang-Mills gauge field /." [Hong Kong : University of Hong Kong], 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13671728.
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Kovalev, Alexei Gennadievich. "The geometry of dimensionally reduced anti-self-duality equations." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282324.
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Alvarez, José Luis Alejo. "Electric-magnetic duality in N = 2 supersymmetric gauge theory /." São Paulo, 2015. http://hdl.handle.net/11449/154699.
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Orientador: Nathan Jacob Berkovits<br>Banca: Horatiu Stefan Nastase<br>Banca: Diego Trancanelli<br>Resumo: Nesta dissertação apresentamos uma descrição da dualidade elétrica-magnética e seus aspectos clássicos e quânticos. Nosso análise se inicia com os monopolos magéticos sugeridos por Dirac em 1931[1] e vai até o trabalho do Seiberg e Witten em 1994 [27]. Na descrição clássica, precisamos introduzir os monopolos magnéticos a fim de obter a dualidade elétrica-magnética manifesta. Mais tarde, a origem dos monopolos se mais torna mais clara quando começamos com uma teoria de Yang-Mills. Os aspectos clássicos da teoria foram explicados pela conjetura de Montonen e Olive 1977 [7]. Explorando os aspectos quânticos da teoria, notamos a importância de introduzir supersimetria, principalmente supersimetria estendida, onde tiramos vantagem da propiedade de holomorficidade, a qual nos leva aos teoremas não renormalizáveis, onde o cálculo é mais simples. Focamos na teoria de gauge supersimétrica N = 2 SU(2). A teoria é completamente resolvível para baixas energias. A maior parte do conteúdo deste trabalho é baseada nas várias revisões da dualidade de Seiberg-Witten [30],[31],[32]<br>Abstract: In this dissertation we present a description of the electric-magnetic duality and their classical and quantum aspects. Our analysis starts from the suggested magnetic monopoles by Dirac in 1931 [1] and goes until the work of Seiberg and Witten in 1994 [27]. In the classical description, we need to introduce the magnetic monopoles in order to make manifest the electricmagnetic duality. Later, the origin of monopoles becomes clear when we start from a Yang-Mills theory. The classical aspects of the E-M duality are covered in the Montonen-Olive conjecture 1977[7]. Working on the quantum aspects of the theory, we note the importance of introducing supersymmetry. Specially for extended supersymmetry, where we take advantage of the holomorphicity property, which leads us to the non-renormalizable theorems, where the computation is easier. We focus on theN = 2SU(2) supersymmetric gauge theories. It turns out that the theory is fully solvable at the low energies regime[27]. Most of this work is based on reviews about the Seiberg and Witten duality [30],[31],[32]<br>Mestre
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Alvarez, José Luis Alejo [UNESP]. "Electric-magnetic duality in N = 2 supersymmetric gauge theory." Universidade Estadual Paulista (UNESP), 2015. http://hdl.handle.net/11449/154699.
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Made available in DSpace on 2018-07-27T18:26:08Z (GMT). No. of bitstreams: 0
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000866848.pdf: 631406 bytes, checksum: 951f24cae0a92bf26987f68a9faaef16 (MD5)<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>Nesta dissertação apresentamos uma descrição da dualidade elétrica-magnética e seus aspectos clássicos e quânticos. Nosso análise se inicia com os monopolos magéticos sugeridos por Dirac em 1931[1] e vai até o trabalho do Seiberg e Witten em 1994 [27]. Na descrição clássica, precisamos introduzir os monopolos magnéticos a fim de obter a dualidade elétrica-magnética manifesta. Mais tarde, a origem dos monopolos se mais torna mais clara quando começamos com uma teoria de Yang-Mills. Os aspectos clássicos da teoria foram explicados pela conjetura de Montonen e Olive 1977 [7]. Explorando os aspectos quânticos da teoria, notamos a importância de introduzir supersimetria, principalmente supersimetria estendida, onde tiramos vantagem da propiedade de holomorficidade, a qual nos leva aos teoremas não renormalizáveis, onde o cálculo é mais simples. Focamos na teoria de gauge supersimétrica N = 2 SU(2). A teoria é completamente resolvível para baixas energias. A maior parte do conteúdo deste trabalho é baseada nas várias revisões da dualidade de Seiberg-Witten [30],[31],[32]<br>In this dissertation we present a description of the electric-magnetic duality and their classical and quantum aspects. Our analysis starts from the suggested magnetic monopoles by Dirac in 1931 [1] and goes until the work of Seiberg and Witten in 1994 [27]. In the classical description, we need to introduce the magnetic monopoles in order to make manifest the electricmagnetic duality. Later, the origin of monopoles becomes clear when we start from a Yang-Mills theory. The classical aspects of the E-M duality are covered in the Montonen-Olive conjecture 1977[7]. Working on the quantum aspects of the theory, we note the importance of introducing supersymmetry. Specially for extended supersymmetry, where we take advantage of the holomorphicity property, which leads us to the non-renormalizable theorems, where the computation is easier. We focus on theN = 2SU(2) supersymmetric gauge theories. It turns out that the theory is fully solvable at the low energies regime[27]. Most of this work is based on reviews about the Seiberg and Witten duality [30],[31],[32]
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Slizovskiy, Sergey. "Yang-Mills Theory in Gauge-Invariant Variables and Geometric Formulation of Quantum Field Theories." Doctoral thesis, Uppsala universitet, Teoretisk fysik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-129670.
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In Part I we are dealing with effective description of Yang-Mills theories based on gauge-invarint variables. For pure Yang-Mills we study the spin-charge separation varibles. The dynamics in these variables resembles the Skyrme-Faddeev model. Thus the spin-charge separation is an important intermediate step between the fundamental Yang-Mills theory and the low-energy effective models, used to model the low-energy dynamics of gluons. Similar methods may be useful for describing the Electroweak sector of the Standard Model in terms of gauge-invariant field variables called supercurrents. We study the geometric structure of spin-charge separation in 4D Euclidean space (paper III) and elaborate onconnection with gravity toy model. Such reinterpretation gives a way to see how effective flat background metric is created in toy gravity model by studying the appearance of dimension-2 condensate in the Yang-Mills (paper IV). For Electroweak theory we derive the effective gauge-invariant Lagrangian by doing the Kaluza-Klein reduction of higher-dimensional gravity with 3-brane, thus making explicit the geometric interpretation for gauge-invariant supercurrents. The analogy is then made more precise in the framework of exact supergravity solutions. Thus, we interpret the Higgs effect as spontaneous breaking of Kaluza-Klein gauge symmetry and this leads to interpretation of Higgs field as a dilaton (papers I and II). In Part II of the thesis we study rather simple field theories, called “geometric” or “instantonic”. Their defining property is exact localization on finite-dimensional spaces – the moduli spaces of instantons. These theories allow to account exactly for non-linearity of space of fields, in this respect they go beyond the standard Gaussian perturbation theory. In paper V we show how to construct a geometric theory of chiral boson by embedding it into the geometric field theory. In Paper VI we elaborate on the simplest geometric field theory – the supersymmetric Quantum Mechanics and construct new non-perturbative topological observables that have a transparent meaning both in geometric and in the Hamiltonian formalisms. In Paper VII we are motivated by making perturbations away from the simple instantonic limit. For that we need to carefully define the observables that are quadratic in momenta and develop the way to compute them in geometric framework. These correspond geometrically to bivector fields (or, in general, the polyvector fields). We investigate the local limit of polyvector fields and compare the geometric calculation with free-field approach.
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Jones, Martyna Maria. "Form factors and scattering amplitudes in supersymmetric gauge theories." Thesis, Queen Mary, University of London, 2018. http://qmro.qmul.ac.uk/xmlui/handle/123456789/53582.
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The study of scattering amplitudes in the maximally supersymmetric Yang-Mills theory (N = 4 SYM) is a thriving field of research. Since the reformulation of perturbative gauge theory as a twistor string theory by Witten, this area has witnessed a flurry of activity, leading to the discovery of a multitude of novel techniques, such as recursion relations and MHV diagrams, collectively referred to as on-shell methods. In parallel, many previously hidden properties and rich mathematical structures have been found, a powerful example of such being the dual superconformal symmetry. It is natural to ask whether this understanding can be extended to phenomenologically relevant theories as well as other quantities. The goal of the present work is to apply the modern on-shell methods to calculations of form factors, with particular focus on those which are relevant for describing Higgs production in QCD from the point of view of an effective field theory. Specifically, our analysis will be carried out in supersymmetric gauge theories at two-loop level and will consist of several steps. We focus first on operators in the SU(2j3) closed subsector of N = 4 SYM, in particular two non-protected, dimension-three operators. We then move on to consider the trilinear operator Tr(F3) and a related descendant of the Konishi operator which contains Tr(F3), also in N =4 SYM. Finally, we concentrate on two-loop form factors of these two operators in theories with less-than-maximal supersymmetry. The result of our investigation shows an emergence of a small number of universal building blocks, ultimately related to the two-loop form factor of a trilinear half-BPS operator. This finding suggests that the most complicated, maximally transcendental part of Higgs plus multi-gluon amplitudes in QCD can be equivalently computed in a remarkably simple way by considering form factors of half-BPS operators in N =4 SYM.
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Lumia, Luca. "Digital quantum simulations of Yang-Mills lattice gauge theories." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/22355/.
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I metodi di calcolo tradizionali per le teorie di gauge su reticolo risultano problematici in regioni di diagrammi di fase a grandi valori del potenziale chimico o quando sono utilizzate per riprodurre la dinamica in tempo reale di un modello. Tali problemi possono essere evitati da simulazioni quantistiche delle teorie di gauge su reticolo, le quali stanno diventando sempre più riproducibili sperimentalmente, grazie ai recenti progressi tecnologici. In questa tesi formuliamo una versione delle teorie di Yang-Mills su reticolo appropriata per risolvere il problema della dimensione infinita dello spazio di Hilbert associato ai bosoni di gauge. Questa formulazione è adatta per essere riprodotta in un simulatore quantistico e ne implementiamo una completa simulazione su un computer quantistico digitale, sfruttando il framework Qiskit. In questa simulazione misuriamo le energie del ground state e i valori di aspettazione di alcuni Wilson loop al variare dell'accoppiamento della teoria, per studiarne le fasi e valutare la prestazione dei metodi usati.
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Endres, Michael G. "Topics in lattice field theory /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/9713.
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Stiffler, Kory M. "A walk through superstring theory with an application to Yang-Mills theory: k-strings and D-branes as gauge/gravity dual objects." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/744.
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Superstring theory is one current, promising attempt at unifying gravity with the other three known forces: the electromagnetic force, and the weak and strong nuclear forces. Though this is still a work in progress, much effort has been put forth toward this goal. A set of specific tools which are used are gauge/gravity dualities. This thesis consists of a specific implementation of gauge/gravity dualities to describe k-strings of strongly coupled gauge theories as objects dual to Dpbranes embedded in confining supergravity backgrounds from low energy superstring field theory.
Along with superstring theory, k-strings are also commonly investigated with lattice gauge theory and Hamiltonian methods. A k$string is a colorless combination of quark-anti-quark source pairs, between which a color flux tube develops. The two most notable terms of the k-string energy are, for large quark anti-quark separation L, the tension term, proportional to L, and the Coulombic 1/L correction, known as the Luscher term.
This thesis provides an overview of superstring theories and how gauge/gravity dualities emerge from them. It shows in detail how these dualities can be used for the specific problem of calculating the k-string energy in 2+1 and 3+1 space-time dimensions as the energy of Dp-branes in the dual gravitational theory. A detailed review of k-string tension calculations is given where good agreement is found with lattice gauge theory and Hamiltonian methods. In reviewing the k-string tension, we also touch on how different representations of k-strings can be described with Dp-branes through gauge/gravity dualities. The main result of this thesis is how the Luscher term is found to emerge from the energy calculation of Dp-branes. In 2+1 space-time dimensions, we have Luscher term data to compare with from lattice gauge theory, where we find good agreement.
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Tavares, Gustavo Marques. "Instantons em espaços curvos." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/277048.
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Orientador: Ricardo Antonio Mosna<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin<br>Made available in DSpace on 2018-09-24T14:09:39Z (GMT). No. of bitstreams: 1
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Previous issue date: 2010<br>Resumo: Neste trabalho estudamos os instantons da teoria de Yang-Mills nos espaços de Schwarzs-child e de Reissner-Nordstrom com grupo de gauge SU(2).Instantons são soluções clássicas da teoria de Yang-Mills definida em um espaço com métrica riemanniana (positiva-definida) e com ação finita.
Primeiramente revisamos a formulação geométrica da teoria de Yang-Mills em uma variedade 4-dimensional,identificando os campos de gauge com conexões em um fibrado principal. Em seguida apresentamos os principais resultados clássicos relacionados aos instantons no espaço plano. Na segunda parte da dissertação realizamos um estudo sistemático das soluções da teoria de Yang-Mills nos espaços de Schwarzschild e de Reissner-Nordstrom euclidianos. Esta abordagem nos permitiu descobrir novas famílias de instantons neste contexto.Ainda,os resultados obtidos mostram que o número de famílias de instantons no espaço de Reissner- Nordstrom depende diretamente da carga elétrica que caracteriza esta geometria<br>Abstract: In this work we study instanton solutions of the Yang-Mills theory in Schwarzschild and Reissner-Nordstrom spaces with gauge group SU(2).Instantons are solutions to the classical field equations of Yang-Mills theory defined in a space with Riemannian (positive de finite)metric with finite action. We begin with a review of the geometric setting of Yang-Mills theory on a four dimensional manifold,which relates the gauge fields to connections on a fiber bundle.We proceed by presenting the main results related to instantons in flat space. In the second part of this thesis we perform a systematic study of the solutions of Yang-Mills theory in Euclidian Schwarzschild and Reissner-Nordstrom spaces.This approach led us to discover a new family of instantons de fined in those backgrounds. Moreover, our results show that the number of instanton families in the Reissner-Nordstrom space depends directly on the eletric charge which caracterizes this geometry<br>Mestrado<br>Física das Particulas Elementares e Campos<br>Mestre em Física
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Necco, Silvia. "The static quark potential and scaling behavior of SU(3) lattice Yang-Mills theory." Doctoral thesis, [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=96870672X.
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Bibireata, Daniel. "Super Yang-Mills theories on the lattice." Connect to this title online, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1117586284.
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Thesis (Ph. D.)--Ohio State University, 2005.<br>Title from first page of PDF file. Document formatted into pages; contains x, 94 p.; also includes graphics Includes bibliographical references (p. 52-54). Available online via OhioLINK's ETD Center
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Nolland, David John. "Quantum field theories with fermions in the Schrödinger representation." Thesis, Durham University, 2000. http://etheses.dur.ac.uk/4410/.
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This thesis is concerned with the Schrödinger representation of quantum field theory. We describe techniques for solving the Schrödinger equation which supplement the standard techniques of field theory. Our aim is to develop these to the point where they can readily be used to address problems of current interest. To this end, we study realistic models such as gauge theories coupled to dynamical fermions. For maximal generality we consider particles of all physical spins, in various dimensions, and eventually, curved spacetimes. We begin by considering Gaussian fields, and proceed to a detailed study of the Schwinger model, which is, amongst other things, a useful model for (3+1) dimensional gauge theory. One of the most important developments of recent years is a conjecture by Mal-dacena which relates supergravity and string/M-theory on anti-de-Sitter spacetimes to conformal field theories on their boundaries. This correspondence has a natural interpretation in the Schrödinger representation, so we solve the Schrödinger equation for fields of arbitrary spin in anti-de-Sitter spacetimes, and use this to investigate the conjectured correspondence. Our main result is to calculate the Weyl anomalies arising from supergravity fields, which, summed over the supermultiplets of type JIB supergravity compactified on AdS(_s) x S(^5) correctly matches the anomaly calculated in the conjecturally dual N = 4 SU{N) super-Yang-Mills theory. This is one of the few existing pieces of evidence for Maldacena's conjecture beyond leading order in TV.
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Schuster, Theodor. "Scattering amplitudes in four- and six-dimensional gauge theories." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2014. http://dx.doi.org/10.18452/17034.
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Streuamplituden der Quantenchromodynamik (QCD), N = 4 Super-Yang-Mills-Theorie (SYM-Theorie) und der sechsdimensionalen N = (1, 1) SYM-Theorie werden untersucht, mit einem Fokus auf die Symmetrien und Relationen zwischen den Streuamplituden dieser Eichtheorien auf dem Baum-Niveau. Die Baum-Niveau- und Ein-Schleifen-Farbzerlegung beliebiger QCD-Amplituden in primitive Amplituden wird bestimmt und Identitäten hergeleitet, welche den Nullraum unter den primitiven Amplituden aufspannen. Anschließend wird bewiesen, dass alle farbgeordneten Baum-Niveau-Amplituden der masselosen QCD aus der N = 4 SYM-Theorie erhalten werden können. Analytische Formeln für alle für die QCD relevanten N = 4 SYM-Amplituden werden bestimmt und die Effizienz und Genauigkeit der numerischen Auswertung der analytischen Formeln für farbgeordnete QCD-Baum-Niveau-Amplituden mit einer effizienten numerischen Implementierung der Berends-Giele-Rekursion verglichen. Die Symmetrien der massive Amplituden auf dem Coulomb-Zweig der N = 4 SYM-Theorie werden hergeleitet. Diese können durch eine dimensionale Reduktion der masselosen Baum-Niveau-Amplituden der sechsdimensionalen N = (1, 1) SYM-Theory erhalten werden. Darüber hinaus wird bezeigt, wie es mit Hilfe einer numerischen Implementierung der BCFW-Rekursion möglich ist analytische Formeln für die Baum-Niveau-Superamplituden der N = (1, 1) SYM-Theory zu erhalten und die Möglichkeit eines Uplifts der masselose Baum-Niveau-Amplituden der N = 4 SYM-Theory untersucht. Schließlich wird eine Alternative zur dimensionalen Regularisierung der N = 4 SYM-Theorie untersucht. Die Infrarotdivergenzen werden hierbei durch Massen regularisiert, die durch einen Higgs-Mechanismus erhalten wurden. Die korrespondierende Stringtheorie-Beschreibung deutet auf eine exakte duale konforme Symmetrie der Streuamplituden hin. Durch explizite Rechnungen wird dies bestätigt und Vorteile des Regulators werden demonstriert.<br>We study scattering amplitudes in quantum chromodynamics (QCD), N = 4 super Yang-Mills (SYM) theory and the six-dimensional N = (1, 1) SYM theory, focusing on the symmetries of and relations between the tree-level scattering amplitudes in these three gauge theories. We derive the tree level and one-loop color decomposition of an arbitrary QCD amplitude into primitive amplitudes. Furthermore, we derive identities spanning the null space among the primitive amplitudes. We prove that every color ordered tree amplitude of massless QCD can be obtained from gluon-gluino amplitudes of N = 4 SYM theory. Furthermore, we derive analytical formulae for all gluon-gluino amplitudes relevant for QCD. We compare the numerical efficiency and accuracy of evaluating these closed analytic formulae for color ordered QCD tree amplitudes to a numerically efficient implementation of the Berends-Giele recursion. We derive the symmetries of massive tree amplitudes on the coulomb branch of N = 4 SYM theory, which in turn can be obtained from N = (1, 1) SYM theory by dimensional reduction. Furthermore, we investigate the tree amplitudes of N = (1, 1) SYM theory and explain how analytical formulae can be obtained from a numerical implementation of the supersymmetric BCFW recursion relation and investigate a potential uplift of the massless tree amplitudes of N = 4 SYM theory. Finally we study an alternative to dimensional regularization of N = 4 SYM theory. The infrared divergences are regulated by masses obtained from a Higgs mechanism. The corresponding string theory set-up suggests that the amplitudes have an exact dual conformal symmetry. We confirm this expectation and illustrate the calculational advantages of the massive regulator by explicit calculations.
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De, Martino Marcelo Gonçalves 1986. "Teoria de calibre em dimensões dois e quatro." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306013.
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Orientador: Marcos Benevenuto Jardim<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-19T09:52:31Z (GMT). No. of bitstreams: 1
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Previous issue date: 2012<br>Resumo: Este trabalho procurou apresentar os conhecimentos básicos necessários para trabalhar com a teoria de calibre em baixas dimensões e também mostrar algumas aplicações da mesma. Na parte básica da teoria, além de comentar aspectos da teoria de Hodge para variedades compactas, também se discute, com certo nível de detalhes, os conceitos de fibrados vetoriais e conexões, com ênfase dada para os cálculos locais com conexões e curvaturas. Duas aplicações mais concretas da teoria de calibre são apresentadas nesta dissertação. Primeiro, em dimensão quatro, discute-se a equação de Yang-Mills sobre 4-variedades e é apresentada uma solução para a equação anti-auto-dual, solução esta que é conhecida na literatura como ansatz de 't Hooft. Por fim, é apresentada a prova, baseado no artigo [DONALDSON, 1983], de um importante teorema devido a M. S. Narasimhan e C. S. Seshadri que relaciona os conceitos de estabilidade com o de existência de conexão unitária satisfazendo certa propriedade, em fibrados vetoriais complexos sobre superfícies de Riemann<br>Abstract: In this work it is developed the basic knowledge required to deal with gauge theory in low dimension and it is shown some applications of this theory. Regarding the basic knowledge, apart from discussing some aspects of Hodge theory over compact manifolds, it is also covered, with a certain deal of details, the concepts of vector bundles and connections, paying close attention to the local computations regarding connections and curvature. As for the applications of the theory, we start, in dimension four, by treating the Yang-Mills equation over 4-manifolds and it is showed a solution to the anti-self-dual Yang-Mills equation, solution that is known in the literature as the 't Hooft ansatz. At last, it is given a proof, following the paper [DONALDSON, 1983], of an important theorem due to M. S. Narasimhan and C. S. Seshadri that relates the algebro-geometric notion of stability to the differential-geometric notion of existence of unitary connection whose curvature satisfies a certain condition, on vector bundles over Riemann surfaces<br>Mestrado<br>Matematica<br>Mestre em Matemática
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Engquist, Johan. "Dualities, Symmetries and Unbroken Phases in String Theory : Probing the Composite Nature of the String." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5902.
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Austing, Peter. "Yang-Mills matrix theory." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365336.
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Contatto, Felipe. "Vortices, Painlevé integrability and projective geometry." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/275099.
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GaugThe first half of the thesis concerns Abelian vortices and Yang-Mills theory. It is proved that the 5 types of vortices recently proposed by Manton are actually symmetry reductions of (anti-)self-dual Yang-Mills equations with suitable gauge groups and symmetry groups acting as isometries in a 4-manifold. As a consequence, the twistor integrability results of such vortices can be derived. It is presented a natural definition of their kinetic energy and thus the metric of the moduli space was calculated by the Samols' localisation method. Then, a modified version of the Abelian–Higgs model is proposed in such a way that spontaneous symmetry breaking and the Bogomolny argument still hold. The Painlevé test, when applied to its soliton equations, reveals a complete list of its integrable cases. The corresponding solutions are given in terms of third Painlevé transcendents and can be interpreted as original vortices on surfaces with conical singularity. The last two chapters present the following results in projective differential geometry and Hamiltonians of hydrodynamic-type systems. It is shown that the projective structures defined by the Painlevé equations are not metrisable unless either the corresponding equations admit first integrals quadratic in first derivatives or they define projectively flat structures. The corresponding first integrals can be derived from Killing vectors associated to the metrics that solve the metrisability problem. Secondly, it is given a complete set of necessary and sufficient conditions for an arbitrary affine connection in 2D to admit, locally, 0, 1, 2 or 3 Killing forms. These conditions are tensorial and simpler than the ones in previous literature. By defining suitable affine connections, it is shown that the problem of existence of Killing forms is equivalent to the conditions of the existence of Hamiltonian structures for hydrodynamic-type systems of two components.
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Peng, Zongren. "Topics in N = Yang-Mills theory." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2012. http://tel.archives-ouvertes.fr/tel-00834200.
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Cette thèse décrit quelques développements dans les techniques de calcul des amplitudes de diffusion en théorie supersymétrique de champ de jauge . L'accent est mis sur les relations de récurrence on-shell et sur l'utilisation de méthodes d'unitarité pour des calculs de boucle. En particulier, la récurrence on-shell est liée aux règles BCFW pour calculer les amplitudes de jauge au niveau des arbres. Les combinaisons de techniques de coupe d'unitarité et la récurrence sont utilisées pour calculer les amplitudes de boucle, et finalement, à partir des amplitudes, pour obtenir la fonction de corrélation énergie-énergie en théorie de super-Yang-Mills N = 4 à l'aide de la représentation de Mellin-Barnes. Dans le dernier chapitre, nous tentons de trouver un contour convergent pour les intégrales de Mellin Barnes en multi-dimension obtenu par une certaine approximation d'un contour de phase stationnaire.
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Hong, Ying-Ji. "Adiabatic limits in Yang-Mills theory." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.337735.
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Barnich, Glenn. "Local BRST cohomology in Yang-Mills theory." Doctoral thesis, Universite Libre de Bruxelles, 1995. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212605.
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Svensk, Linnea. "Localization Techniques, Yang-Mills Theory and Strings." Thesis, Uppsala universitet, Teoretisk fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-280740.
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Equivariant localization techniques exploit symmetries of systems, represented by group actions on manifolds, and use them to evaluate certain partition functions exactly. In this master thesis we begin with the study of localization in finite dimensions. We then generalize this concept to infinite dimensions and study the partition function of two dimensional quantum Yang- Mills theory and its relation to string theory. The partition function can be written as a sum over the critical point set and be related to the topology of the moduli space of flat connections. Furthermore, for large N the partition function of the gauge groups SU(N) and U(N) can be interpreted as a string perturbation series. The coefficients of the expansion are given by a sum over maps from a two dimensional surface onto the two dimensional target space and thus the partition function is interpreted as a closed string theory. Also, a string theory action is discussed using topological field theory tools and localization techniques.
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Sieg, Christoph. "Aspects of noncommutativity and holography in field theory and string theory." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=974396095.
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Barresi, Andrea. "SO(3) Yang-Mills theory on the lattice." Doctoral thesis, [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968943675.
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Jiang, Wen. "Aspects of Yang-Mills theory in twistor space." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:4f6bc303-e8d9-4004-ab90-56b85cd917c0.
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This thesis carries out a detailed investigation of the action for pure Yang-Mills theory which L. Mason formulated in twistor space. The rich structure of twistor space results in greater gauge freedom compared to the theory in ordinary space-time. One particular gauge choice, the CSW gauge, allows simplifications to be made at both the classical and quantum level. The equations of motion have an interesting form in the CSW gauge, which suggests a possible solution procedure. This is explored in three special cases. Explicit solutions are found in each case and connections with earlier work are examined. The equations are then reformulated in Minkowski space, in order to deal with an initial-value, rather than boundary-value, problem. An interesting form of the Yang-Mills equation is obtained, for which we propose an iteration procedure. The quantum theory is also simplified by adopting the CSW gauge. The Feynman rules are derived and are shown to reproduce the MHV diagram formalism straightforwardly, once LSZ reduction is taken into account. The three-point amplitude missing in the MHV formalism can be recovered in our theory. Finally, relations to Mansfield’s canonical transformation approach are elucidated.
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Sikorowski, Jakub. "Correlation functions in maximally supersymmetric Yang-Mills theory." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:1257e3bc-5f1d-4896-8859-a5544ce8ac97.
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In this thesis we consider the planar maximally supersymmetric Yang-Mills theory. First, we look at the correlation function of a null Wilson loop with four edges and a local operator at weak coupling. We use the Lagrangian insertion technique to find the integral representation up to two loops. Performing the integrals with a method closely linked to the dual space formalism for the scattering amplitudes, we explicitly compute the two loop result. We demonstrate the connection between the calculated observable and the cusp anomalous dimension by recovering the three loop value of the cusp anomalous dimension. We also explore the advantages of expressing the loop integrand in twistor variables. The second observable we look at is the four point correlation function of the BMN operators on a line at strong coupling. In order to access this regime we perform a semi-classical computation in the classical string theory. Considering area of an extended minimal surface stretched between the four operators, we find two different saddle points. We show that the extended minimal surface is sub-dominant to the saddle point composed of three geodesic strings joining the four operators in a sequence. The result is that, to the leading order at strong coupling, the considered correlation function is equal to its tree-level value when all operators are on a line.
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Yildirim, Tuna. "Topologically massive Yang-Mills theory and link invariants." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1519.
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In this thesis, topologically massive Yang-Mills theory is studied in the framework of geometric quantization. This theory has a mass gap that is proportional to the topological mass m. Thus, Yang-Mills contribution decays exponentially at very large distances compared to 1/m, leaving a pure Chern-Simons theory with level number k. The focus of this research is the near Chern-Simons limit of the theory, where the distance is large enough to give an almost topological theory, with a small contribution from the Yang-Mills term. It is shown that this almost topological theory consists of two copies of Chern-Simons with level number k/2, very similar to the Chern-Simons splitting of topologically massive AdS gravity model. As m approaches to infinity, the split parts add up to give the original Chern-Simons term with level k. Also, gauge invariance of the split CS theories is discussed for odd values of k. Furthermore, a relation between the observables of topologically massive Yang-Mills theory and Chern-Simons theory is obtained. It is shown that one of the two split Chern-Simons pieces is associated with Wilson loops while the other with 't Hooft loops. This allows one to use skein relations to calculate topologically massive Yang-Mills theory observables in the near Chern-Simons limit. Finally, motivated with the topologically massive AdS gravity model, Chern-Simons splitting concept is extended to pure Yang-Mills theory at large distances. It is shown that pure Yang-Mills theory acts like two Chern-Simons theories with level numbers k/2 and -k/2 at large scales. At very large scales, these two terms cancel to make the theory trivial, as required by the existence of a mass gap.
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Wagner, Marc. "The pseudoparticle approach in SU(2) Yang-Mills theory." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980706645.
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Wren, Ken Kangda. "Constrained quantization of Yang-Mills theory via Rieffel induction." Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411178.
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Freyhult, Lisa. "Aspects of Yang-Mills Theory : Solitons, Dualities and Spin Chains." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-4498.
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Lundin, Jim. "Electromagnetic Duality in SO(3) Yang-Mills Theory : Bachelor Thesis." Thesis, Uppsala universitet, Teoretisk fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-354716.
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We introduce the historical context and motivation for the search for magnetic monopoles or monopole-like objects. Beginning the theoretical part we investigate the properties of groups as they relate to symmetries in physical theories. Using this as a basis we investigate the requirements for global and local gauge invariance for a scalar field, the latter giving the non-trivial connection to a gauge field. From this we present the Georgi-Glashow model and develop its particle spectrum using the connected Higgs field and its associated Higgs mechanism. We then present the electromagnetic duality by extending the Maxwell's equations toinclude magnetic sources. Using the assumption of magnetic sources we present the Dirac quantization condition, motivating the quantization of electric charge. Returning to our model we present the 't Hooft-Polyakov ansatz and investigate its defining properties as a finite energy soliton in our Higgs field. We show the magnetic properties and motivate its validity as a monopole like object. Continuing we define BPS-states on the lower bound for the mass of a monopole like object with magnetic and electric charge. Giving a BPS monopole as a solution in the vein of 't Hooft and Polyakov. Returning to the electromagnetic duality we propose the Montonen-Olive conjecture by exchanging massive vector bosons in our model with the BPS monopoles we developed. We shortly comment on evident problems and present supersymmetry as a possible solution. Finally we present the Witten Effect by allowing a CP violating term in our Lagrangian. From this we extend the Montonen-Olive conjecture to include invariance under the SL(2,Z) group.
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Efremov, Alexander. "Renormalization of SU(2) Yang-Mills theory with flow equations." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX050/document.
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L'objectif de ce travail est une construction perturbative rigoureuse de la théorie de la Yang-Mills SU(2) dans l'espace euclidien à quatre dimensions. La technique d'intégration fonctionnelle donne une basemathématique pour établir les équations de flot différentielles du groupe de renormalisation pour l'action efficace. Si l'introduction de régulateurs dans l'espace de moments permet de donner une définition mathématique des fonctions de Schwinger, la difficulté importante de l'approche est le fait que cesrégulateurs brisent l'invariance de jauge. Ainsi, le travail principal est alors de prouver à tous les ordres en perturbation l'existence de ces fonctions de correlation et la validité des identités de Slavnov-Taylor pour la théorie renormalisée<br>The goal of this work is a rigorous perturbative construction of the SU(2) Yang-Mills theory in four dimensional Euclidean space. The functional integration technique gives a mathematical basis for establishing the differential Flow Equations of the renormalization group for the effective action. While the introduction of momentum space regulators permits to give a mathematical definition of the Schwinger functions, the important difficulty of the approach is the fact that these regulators break gauge invariance. Thus the main part of the work is to prove at all loop orders the existence of the vertex functions and the restoration of the Slavnov-Taylor identities in the renormalised theory
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Guo, Bin. "Lollipop diagrams in defect N=4 super Yang-Mills theory." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/62717.
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In this thesis, we have studied the lollipop diagrams in defect $\mathcal{N}$=4 super Yang-Mills field theory with nontrivial background, which is dual to the D3-D5 brane system with the probe D5 brane carrying k units of flux. Using the framework for performing loop computations for this system built by Buhl-Mortensen, Leeuw, Ipsen, Kristjansen and Wilhelm, we prove that for arbitrary N and k, the contribution of the lollipop diagrams to the one-point function is zero. This improves their result, where they take the planar limit N>>1 and the probe brane limit k/N<<1.<br>Science, Faculty of<br>Physics and Astronomy, Department of<br>Graduate
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Brits, Lionel. "Hamiltonian treatment of the (2+1)-dimensional Yang-Mills theory." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/31435.
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The (2+l)-dimensional Yang-Mills theory is studied in the functional Schrödinger formalism using the machinery laid out by Karabali and Nair. The low-lying spectrum of the theory is computed by analyzing correlators of the Leigh-Minic-Yelnikov ground-state wave-functional in the Abelian limit. The contribution of the WZW measure is treated by a controlled approximation and the resulting spectrum is shown to reduce to that obtained by Leigh et al., at large momentum. The inclusion of fundamental Fermions is done from first-principles, and it is found that the requirement of gauge invariance spoils the commutativity between gauge and matter fields.<br>Science, Faculty of<br>Physics and Astronomy, Department of<br>Graduate
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Ohki, Hiroshi. "Chiral four dimensional field theory from superstring and higher dimensional super Yang-Mills theory." 京都大学 (Kyoto University), 2010. http://hdl.handle.net/2433/120647.
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Tennert, Oliver. "Vortex condensation and confinement in centre projected lattice Yang-Mills theory." [S.l. : s.n.], 2000. http://deposit.ddb.de/cgi-bin/dokserv?idn=963188941.
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Barrett, John William. "The holonomy description of classical Yang-Mills theory and general relativity." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37629.
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Monteiro, Gustavo Machado [UNESP]. "MHV tree amplitudes in super-Yang-Mills and in superstring theory." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/99169.
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monteiro_gm_me_ift.pdf: 337936 bytes, checksum: ea2742967e22f6ceedb3f47bd956fbfb (MD5)<br>Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)<br>A presente dissertação trata-se de uma revisão sobre amplitudes MHV na teoria de Yang-Mills e em sua extensão maximalmente supersimétrica. A demonstração da fórmula geral para tais amplitudes é dada no terceiro capítulo. Uma vez que o formalismo de twistors se apresenta como um interessante arcabouço teórico para o estudo de tais amplitudes, uma discussão sobre o mesmo e considerada, bem como sua extensão supersimétrica. Ao final, o cálculo de quatro e cinco pontos para amplitudes MHV em teoria de supercordas é apresentado. Para tal, foi utilizada a prescrição fornecida por Berkovits e Maldacena em [11]<br>In the present work, we have provided a review about MHV amplitudes in Yang- Mills and maximally supersymmetric Yang-Mills theory. A proof of MHV formula was given in the third chapter. Since twistor formalism provides an interesting framework to study such amplitudes, a discussion about it is also considered as well as its supersymmetric extension. At the end, we have computed MHV four-point and ve-point gluon tree amplitudes in superstring theory, using a prescription given by Berkovits and Maldacena [11]
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Monteiro, Gustavo Machado. "MHV tree amplitudes in super-Yang-Mills and in superstring theory /." São Paulo : [s.n.], 2010. http://hdl.handle.net/11449/99169.
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Orientador: Nathan Jacob Berkovits<br>Banca: Horatiu Stefan Nastase<br>Banca: Vladimir Demyanovich Pershin<br>Resumo: A presente dissertação trata-se de uma revisão sobre amplitudes MHV na teoria de Yang-Mills e em sua extensão maximalmente supersimétrica. A demonstração da fórmula geral para tais amplitudes é dada no terceiro capítulo. Uma vez que o formalismo de twistors se apresenta como um interessante arcabouço teórico para o estudo de tais amplitudes, uma discussão sobre o mesmo e considerada, bem como sua extensão supersimétrica. Ao final, o cálculo de quatro e cinco pontos para amplitudes MHV em teoria de supercordas é apresentado. Para tal, foi utilizada a prescrição fornecida por Berkovits e Maldacena em [11]<br>Abstract: In the present work, we have provided a review about MHV amplitudes in Yang- Mills and maximally supersymmetric Yang-Mills theory. A proof of MHV formula was given in the third chapter. Since twistor formalism provides an interesting framework to study such amplitudes, a discussion about it is also considered as well as its supersymmetric extension. At the end, we have computed MHV four-point and ve-point gluon tree amplitudes in superstring theory, using a prescription given by Berkovits and Maldacena [11]<br>Mestre
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Warrick, Edmund. "A canonical basis approach to unitarity calculations in Yang-Mills theories." Thesis, Swansea University, 2011. https://cronfa.swan.ac.uk/Record/cronfa43123.
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A Canonical Basis m ethod is presented for computing the cut-constructible parts of loop amplitudes in massless Yang-Mills theory by generalised Unitarity. The method relies upon constructing a canonical basis of general cut solutions and constructing the amplitude by identifying the integral coefficients with elements of the canonical basis, thereby avoiding repeated integration of similar integrand structures. The method provides closed, rational, fully analytic expressions for the integral coefficients. As an application the m ethod is applied to compute the previously unknown NMHV partial amplitudes of the 7-gluon Af = 1 chiral multiplet loop, and is then extended to rederive the cut-constructible terms of the NMHV 6-gluon partial amplitudes with a complex scalar loop.
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Peetz, Roland. "Spectrum of N=1 super Yang Mills theory on the lattice with a light gluino." [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=97018249X.
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Wainwright, P. R. "Nahm's equation and the search for classical solutions in Yang-Mills theory." Thesis, Durham University, 1987. http://etheses.dur.ac.uk/6652/.
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The history of the theory of magnetic monopoles in classical electrodynamics and unified gauge theories is reviewed, and the Atiyah-Ward and Atiyah-Drinfe1d-Hitchin-Man in constructions of exact classical solutions to the self-dual Yang-Mills equations are described. It is shown that the one-dimensional self-dual equation introduced by Nahm can be reformulated as a Rieraann-Hi1bert problem through the twister transform previously used by Ward for monopole and instanton fields, and a general formula for the patching matrix is derived. This is evaluated in some special cases, and a few simple examples are given where Nahm's equation can be solved by this method. An attempt is made to generalize the ADHM construction to treat non self dual Yang-Mills fields, with only partial success. The one-dimensional analogue of the second-order Yang-Mills equation, the so-called non self dual Nahm equation, is investigated, paying particular attention to a simple ansatz in which translation of the fields is equivalent to a mere scale transformation of the matrices T(_i)(Z). For these 'separable solutions' the matrices satisfy certain cubic equations, whose solution space depends critically on the nature of the Lie algebra under consideration. It is shown that corresponding to certain Riemannian symmetric pairs there are one-parameter families of 'interpolating solutions' to the cubic equations, which join oppositely oriented bases of a Lie subalgebra. The associated matrix-valued functions T(_i)(z) therefore interpolate between solutions of 'selfdual' and 'antiselfdual' Nahm equations.
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Eden, Burkhard. "Correlation functions in N=2 and N=4 supersymmetric Yang-Mills theory." Thesis, King's College London (University of London), 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312972.
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