Academic literature on the topic 'String Theory Quantum Field Theories'

In dieser Dissertation werden Aspekte von superkonformen Quantenfeldtheorien untersucht, die für die sogenannte AdS/CFT Korrespondenz relevant sind. Die AdS/CFT Korrespondenz beschreibt eine Dualität zwischen Stringtheorien im Anti-de Sitter Raum und superkonformen Quantenfeldtheorien im Minkowskiraum. In diesem Kontext wurde die sog. Wilsonschleifen / Amplituden Dualität entdeckt, die die Übereinstimmung von n-Gluon MHV Amplituden und n-seitigen polygonalen Wilsonschleifen in der N=4 supersymmetrischen Yang-Mills (SYM) Theorie beschreibt. Im ersten Teil dieser Dissertation wird die Wilsonschleifenseite einer solchen möglichen Dualität in der N=6 superkonformen Chern-Simons (ABJM) Theorie untersucht. Das Hauptergebnis dieser Untersuchungen ist, dass der Erwartungswert der n-seitigen polygonalen Wilsonschleifen auf Einschleifenebene verschwindet, während er auf Zweischleifenebene in seiner funktionalen Form identisch zu der analogen Wilsonschleife in N=4 SYM auf Einschleifenniveau ist. Außerdem wird eine anomale konforme Wardidentität für Wilsonschleifen in Chern-Simons Theorie berechnet. Zudem werden die damit im Zusammenhang stehenden Entwicklungen für Amplituden und Korrelatoren in der ABJM Theorie diskutiert. Im zweiten Teil dieser Dissertation werden Dreipunktfunktionen von zwei geschützten Operatoren und einem Twist-Zwei Operator mit beleibigem Spin j in der N=4 SYM Theorie berechnet. Dafür werden die Indizes des Spin j Operators auf den Lichtkegel projiziert und der Korrelator wird in einem Grenzfall untersucht in dem der Impuls der bei dem Spin j Operator einfließt verschwindet. Dieser Grenzfall vereinfacht die perturbative Berechnung erheblich, da alle Dreipunktdiagramme effektiv auf Zweipunktdiagramme reduziert werden und die Abhängigkeit der Mischungsmatrix auf Einschleifenebene herausfällt. Das Ergebnis stimmt mit der Analyse der Operatorproduktentwicklung von Vierpunktfunktionen geschützter Operatoren von Dolan und Osborn aus dem Jahre 2004 überein.<br>In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investivated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop / amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N =4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 185-194).<br>In this thesis, we use string theory constructions and dualities to explore various features of interacting quantum field theories. We begin with an overview in Chapter 1, of past and recent developments in quantum field theories, explaining the advantages of string theoretic techniques over traditional approaches in answering a range of questions about interacting dynamics. In Chapter 2 we study the holographic duality between the 6d (1, 1) Ak-1 little string theory (LST) and type II string theory in the double scaled limit. By identifying the low energy states, which are Cartan gluons in the 6d maximal super-Yang-Mills (SYM) that describes the massless sector of the LST, we compute the four-point amplitudes from both sides of the duality and demonstrate matching results. Since the two computations concern different regimes in the parameter space, their amazing agreement implies the presence of certain nonrenormalization theorems in the 6d SYM. In Chapter 3, motivated by the AdS/CFT duality, we develop a systematic procedure to derive an off-shell action for hydrodynamics from classical Einstein gravity. We first identity the boundary fluid degrees of freedom in the hydrodynamic regime, in terms of gapless modes of the metric in the bulk gravity. This allows us to derive an off-shell action, for relativistic fluids that have gravity duals, at leading order in derivative expansion, by explicitly integrating out gapped degrees of freedom in the bulk. We also explain the strategy to incorporate dissipation and higher order effects. In Chapter 4, we discuss 4d N = 2 superconformal field theories (SCFT) of the Argyres-Douglas (AD) type, which can be constructed in string/M theory by either wrapping M5 branes on punctured Riemann surface or probing 3-fold singularity by IIB string. We classify the punctures (irregular defects in Hitchin system) on the Riemann surface in the former construction, that will give rise to N = 2 SCFTs and demonstrate how to extract exact information about the Coulomb branch spectrum and central charges. We further identify these AD theories constructed from M5 branes with a special class of theories from IIB probing compound Du Val (cDV) singularities, thereby establishing a mathematical connection between singular Hitchin systems and cDV singularities through N = 2 SCFTs. We end with a short summary and outlook for future directions in Chapter 5.<br>by Yifan Wang.<br>Ph. D.

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.

Thesis (Ph. D.)--University of California, San Diego, 2009.<br>Title from first page of PDF file (viewed September 17, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 444-468).

Dans le cadre de la dualité holographique entre une vaste famille de vides 1/2-maximalement supersymétriques Anti-de Sitter à quatre dimensions (AdS₄) et des théories des champs superconformes N=4 supersymétriques à trois dimensions (sCFT₃), nous étudions des questions théoriques majeures de gravité quantique et de théories de jauge. Ce travail a deux directions principales : La premiere partie est consacrée aux mécanismes par lesquels le graviton AdS₄ peut acquérir une petite masse, tandis que la seconde partie concerne la cartographie de la variété superconforme des sCFT₃ considérées. En ce qui concerne la question du mecanisme de Higgs pour le graviton d’AdS₄, nous proposons un nouveau mécanisme qui repose sur le couplage ”faible” de deux sCFT₃s, initialement découplées, en jaugent une symmétrie globale commune. Les deux tenseurs de stress initialement conservés se mélangent et le résultat est une combinaison conservée et une combinaison orthogonale, dont la dimension acquiert une petite dimension anormale. Holographiquement, cette configuration correspond à la connexion de deux univers AdS₄ initialement découplés via un AdS₅ × S⁵ fin, autrement appelé une “gorge” de Janus. Le résultat est une théorie AdS₄-bimétrique, avec un graviton sans masse et un graviton massif, dont la petite masse correspond à la dimension anormale de la combinaison duale de tenseurs de stress. Nous calculons la masse du graviton, qui est exprimée en termes de données géométriques de la ”gorge” de Janus et de l’univers AdS₄ vers zéro, résulte en une théorie de gravité massive dans AdS₄. En ce qui concerne la deuxième direction de ce travail, les déformations superconformes des sCFT₃s considérées qui génèrent la variété superconformale sont des déformations préservant N = 2 supersymétrie, générées par des opérateurs exactement marginaux. Nous présentons comment tous ces opérateurs peuvent être systématiquement extraits de l’index superconforme. Les opérateurs de branche de Coulomb et de Higgs sont pris en compte, tandis qu’une attention particuli ère est accordée aux opérateurs mixtes. On montre que les modules de branches mixtes de ces théories sont des opérateurs à double-corde qui se transforment dans la représentation (Adj, Adj) des groupes de saveursélectriques et magnétiques, modulo un surcomptage pour les quivers avec des noeuds de jauge abéliens. Enfin, nous commentons sur l’interprétation holographique des résultats, en affirmant que les supergravités mesurées peuvent capturer l’espace des modules tout entier si, outre les paramètres de la solution d’arri ère-plan, les modules de quantification des conditions aux limites sontégalement pris en compte<br>Based on the holographic duality between a large class of half-maximally supersymmetric four-dimensional Anti-de Sitter (AdS₄) vacua and three-dimensional N = 4 superconformal field theories (sCFT₃), we study quantum gravitational and gauge theoretic questions. This work has two main directions: The first part is devoted to the mechanisms through which the low-lying AdS₄-graviton can acquire a small mass whereas the second part regards the mapping of the superconformal manifold of the considered sCFT₃s. Regarding the question of the graviton Higgsing in AdS₄, we propose a new mechanism which relies on ”weakly” coupling two initially decoupled sCFT₃s, by gauging a common global symmetry. The two initially conserved stress tensors mix and the result of this mixing is a conserved combination and an orthogonal combination, the scaling dimension of which acquires a small anomalous dimension. Holographically, this setup is dual to connecting two initially decoupled AdS₄ universes via a thin AdS₅ × S⁵ or Janus ”throat”. The result is an AdS₄- bimetric theory, with one massless and one massive graviton, the small mass of which corresponds to the anomalous dimension of the dual stress tensor combination. We compute the mass of the graviton, which is expressed in terms of the geometric data of the Janus ”throat” and of the considered AdS₄ universe. A special decoupling limit of this theory, where the effective four-dimensional gravitational coupling of one of the two universes vanishes, results to an AdS₄-Massive gravity theory. Regarding the second direction of this work, superconformal deformations of the considered sCFT3s which generate the superconformal manifold, are N = 2 supersymmetry preserving deformations, generated by exactly marginal operators. We present how all these operators can be consistently extracted from the superconformal index. Coulomb and Higgs branch operators are considered, while particular attention is payed to mixedbranch operators. It is shown that the mixed-branch moduli of these theories are double-string operators transforming in the (Adj,Adj) representation of the electric and magnetic flavour groups, up to overcounting for quivers with abelian gauge nodes. Finally, we comment on the holographic interpretation of the results, arguing that gauged supergravities can capture the entire moduli space if, in addition to the parameters of the background solution, quantization moduli of boundary conditions are also taken into account

In this project a theoretical study of the so called gyromagnetic ratio was done by investigating classical mechanics, Dirac theory and string theory. The gyromagnetic ratio is a constant term appearing in the coupling between angular momentum and magnetic moment for a particle. A universality in quantum field theory claiming g = 2 regardless of spin is known to exist which also agrees with the found values (g = 2) of the Dirac and string theory. The proof of the aforementioned universality in quantum field theory was sketched in the project by showing that the W-boson Lagrangian is well behaved in the massless limit. Furthermore it is shown that the spin equations of motion for a particle is greatly reduced if g = 2 regardless of spin.<br>I det här projektet utfördes en teoretisk studie av den så kallade gyromagnetsika kvoten genom att undersöka klassisk mekanik, Dirac-teori och strängteori. Den gyromagnetiska kvoten är en konstant term som visar sig i kopplingen mellan rörelsemängsmoment och magnetiskt moment för en partikel. I kvantfältsteori existerar en universalitet som hävdar att g = 2 oberoende av spin. Denna universalitet stämmer överens med de funna värden på g från Dirac-teori och strängtoeri. Beviset för denna universalitet testades genom ett exempel där Lagrangianen för W-bosonen i kvantfältsteori visades bete sig som förväntat när massan för partikeln tilläts gå mot noll. Vidare undersöktes rörelseekvationerna för ett system helt bestämt av dess spin. I dessa kan det visas att ett universellt värde på g oavsett spin reducerar dessa ekvationer avsevärt.

In this thesis we review the gauge/gravity duality and how it can be used to compute the thermodynamic properties and low-energy excitations of holographic quantum liquids - strongly-interacting field theories with a non-zero density of matter. We then study in detail the charge density excitations of two such liquids, the D3/D7 theory and the RN-AdS₄ theory, by computing the poles of their charge density Green's functions, and their charge density spectral functions. Although it is not a Landau Fermi liquid, the charge density excitations of the D3/D7 theory display many of the same properties as one, including a collisionless/hydrodynamic crossover as the temperature is increased. In contrast to this, the charge density (and energy density) excitations of the RN-AdS₄ theory do not share these properties but behave in a way that cannot be explained by Landau's theory of interacting fermionic quasiparticles. This is consistent with other results which indicate that this is not a Landau Fermi liquid.