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Journal articles on the topic 'Dual Lorentzian space'

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Published: 3 June 2025
Last updated: 31 July 2025

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1

Ayylldlz, Nihat, A. Ceylan Çöken, and Ahmet Yücesan. "A CHARACTERIZATION OF DUAL LORENTZIAN SPHERICAL CURVES IN THE DUAL LORENTZIAN SPACE." Taiwanese Journal of Mathematics 11, no. 4 (2007): 999–1018. http://dx.doi.org/10.11650/twjm/1500404798.

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2

Abdel-Baky, Rashad A., and Fatemah Mofarreh. "On an Explicit Characterization of Spherical Curves in Dual Lorentzian 3-Space D 1 3." Mathematical Problems in Engineering 2022 (June 25, 2022): 1–9. http://dx.doi.org/10.1155/2022/3044305.

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In this study, we developed a mathematical framework for studying spherical and null curves in dual Lorentzian 3-space D 1 3 . Considering the causal character of the dual curve, sufficient and necessary conditions for spacelike curves to be dual Lorentzian spherical were given. Also, new sufficient and necessary conditions for non-null curves to be hyperbolic dual spherical were presented. Then, an insight on curves with null-principal normal is reported.
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3

Gürbüz, Nevin, and Ali Görgülü. "On dual r-elastic line." International Journal of Geometric Methods in Modern Physics 11, no. 10 (2014): 1450079. http://dx.doi.org/10.1142/s0219887814500790.

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4

Saglam, Derya, Serhat Ozkan, and Duygu Ozdamar. "SLANT HELICES IN DUAL LORENTZIAN SPACE D3 1." Natural Science and Discovery 2, no. 1 (2016): 3. http://dx.doi.org/10.20863/nsd.04519.

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5

Almoneef, Areej A., and Rashad A. Abdel-Baky. "Timelike Constant Axis Ruled Surface Family in Minkowski 3-Space." Symmetry 16, no. 6 (2024): 677. http://dx.doi.org/10.3390/sym16060677.

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A timelike (TL) constant axis ruled surface in E13 (Minkowski 3-space), as determined by its ruling, forms a constant dual angle with its Disteli-axis (striction axis or curvature axis). In this article, we employ the symmetry through point geometry of Lorentzian dual curves and the line geometry of TL ruled surfaces. This produces the capability to expound a set of curvature functions that specify the local configurations of TL ruled surfaces. Then, we gain some new constant axis ruled surfaces in Lorentzian line space and their geometrical illustrations. Further, we also earn several organiz
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6

Ekinci, Zehra, and H. Hüseyin Uğurlu. "Disteli Diagram of Dual Hyperbolic Spherical Motion in Dual Lorentzian Space." Proceedings of the National Academy of Sciences, India Section A: Physical Sciences 84, no. 3 (2014): 397–407. http://dx.doi.org/10.1007/s40010-014-0149-1.

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7

Machida, Yoshinori, and Hajime Sato. "Twistor spaces for real four-dimensional Lorentzian manifolds." Nagoya Mathematical Journal 134 (June 1994): 107–35. http://dx.doi.org/10.1017/s0027763000004888.

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It is R. Penrose who constructed the twistor theory which gives a correspondence between complex space-times and 3-dimensional complex manifolds called twistor spaces. He and his colleagues investigated conformally invariant equations (e.g. massless field equations, self-dual Yang-Mills equations) on the space-time by transforming them into objects in complex analytical geometry. See e.g. Penrose-Ward [P-W] or Ward-Wells [W-W]. After that, Atiyah-Hitchin-Singer ([A-H-S], cf. [Fr]) constructed the twistor spaces corresponding to real 4-dimensional Riemannian manifolds. Their construction as wel
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8

Ozbey, Emine, and Mehmet Oral. "A STUDY ON RECTIFYING CURVES IN THE DUAL LORENTZIAN SPACE." Bulletin of the Korean Mathematical Society 46, no. 5 (2009): 967–78. http://dx.doi.org/10.4134/bkms.2009.46.5.967.

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9

Abdel-Baky, Rashad A. "Time-like line congruence in the dual Lorentzian 3-space 𝔻13". International Journal of Geometric Methods in Modern Physics 16, № 08 (2019): 1950126. http://dx.doi.org/10.1142/s0219887819501263.

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In this paper, we introduce a time-like line congruence which has the parameter ruled surfaces as principal ruled surfaces. Then we extend several well-known formulae of line congruence in the Euclidean 3-space to the Minkowski 3-space. Meanwhile, we report some geometric descriptions of these formulae. Finally, an example of application is introduced and described in detail.
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10

ABALI, Bahar, and Ahmet YÜCESAN. "Associated curves of a Frenet curve in the dual Lorentzian space." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 1 (2022): 285–304. http://dx.doi.org/10.31801/cfsuasmas.877170.

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11

Özkaldı, Sıddıka, and Halit Gündoğan. "Dual Split Quaternions and Screw Motion in 3-Dimensional Lorentzian Space." Advances in Applied Clifford Algebras 21, no. 1 (2010): 193–202. http://dx.doi.org/10.1007/s00006-010-0236-6.

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12

Önder, Mehmet, and Zehra Ekinci. "On the kinematic interpretation of timelike ruled surfaces." International Journal of Geometric Methods in Modern Physics 12, no. 10 (2015): 1550127. http://dx.doi.org/10.1142/s0219887815501273.

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Timelike ruled surfaces are studied in dual Lorentzian space [Formula: see text] by considering E. Study Mapping and Blaschke frame. A reference timelike ruled surface is considered and associated surfaces are defined. First, it is shown that the surface generated by the instantaneous screw axis (ISA) is a Mannheim offset of reference surface. Later, the kinematic interpretations between these surfaces are introduced by means of Blaschke invariants.
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13

SAYGILI, K. "TOPOLOGICALLY MASSIVE GAUGE THEORY: A LORENTZIAN SOLUTION." International Journal of Modern Physics A 22, no. 16n17 (2007): 2961–76. http://dx.doi.org/10.1142/s0217751x07036361.

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We obtain a Lorentzian solution for the topologically massive non-Abelian gauge theory on AdS space [Formula: see text] by means of an SU (1, 1) gauge transformation of the previously found Abelian solution. There exists a natural scale of length which is determined by the inverse topological mass ν ~ ng2. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an Abelian gauge
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14

Alluhaibi, Nadia, and Rashad A. Abdel-Baky. "Kinematic Geometry of Timelike Ruled Surfaces in Minkowski 3-Space E13." Symmetry 14, no. 4 (2022): 749. http://dx.doi.org/10.3390/sym14040749.

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Symmetry is a frequently recurring theme in mathematics, nature, science, etc. In mathematics, its most familiar manifestation appears in geometry, most notably line geometry, and in other closely related areas. In this study, we take advantage of the symmetry properties of both dual space and original space in order to transfer problems in original space to dual space. We use E. Study Mappingas a direct method for analyzing the kinematic geometry of timelike ruled and developable surfaces. Then, the invariants for a spacelike line trajectory are studied and the well-known formulae of Hamilton
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15

Alluhaibi, Nadia, and R. A. Abdel-Baky. "Kinematic geometry of hyperbolic dual spherical motions and Euler–Savary’s equation." International Journal of Geometric Methods in Modern Physics 17, no. 05 (2020): 2050079. http://dx.doi.org/10.1142/s0219887820500796.

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In this paper, differential properties of the one-parameter hyperbolic dual spherical kinematics are developed with explicit expressions independent of coordinates systems. We calculate Euler–Savary equations of spherical kinematics in the dual Lorentzian 3-space [Formula: see text]. Then from E. Study’s map new proofs are directly attained for the Disteli’s formulae and their spatial equivalents are examined in detail. Lastly for spherical and planar motions, the point trajectories theoretical expressions of the point trajectories are investigated with a certain value of acceleration and velo
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16

Önder, Mehmet, and H. Hüseyin Uğurlu. "On the invariants of Mannheim offsets of timelike ruled surfaces with spacelike rulings." Asian-European Journal of Mathematics 08, no. 01 (2015): 1550009. http://dx.doi.org/10.1142/s1793557115500096.

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In this paper, we give the characterizations for Mannheim offsets of timelike ruled surfaces with spacelike rulings in dual Lorentzian space [Formula: see text]. We obtain the relations between terms of their integral invariants and also we give new characterization for the Mannheim offsets of developable timelike ruled surface. Moreover, we find relations between the area of projections of spherical images for Mannheim offsets of timelike ruled surfaces and their integral invariants.
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17

NERGIZ, SERDAR, and CIHAN SACLIOḠLU. "ON-SHELL THREE-STRING AMPLITUDES AND THE STRUCTURE CONSTANTS OF THE MONSTER LIE ALGEBRA." International Journal of Modern Physics A 05, no. 13 (1990): 2647–65. http://dx.doi.org/10.1142/s0217751x90001203.

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We present the explicit commutator algebra of integrated vertex operators for all states of the bosonic string in 26 dimensions. When the momenta belong to the unique even self-dual lattice Π25,1, this is the Monster Lie algebra M∞ of Borcherds, Conway, Queen and Sloane, containing all other rank 26 Lorentzian algebras. In a string theory process 1 + 2 → 3, the on-shell momenta q1, q2 and q3 are necessarily restricted to an even lattice L in R25,1 as a result of the fact that [Formula: see text]; hence Lorentzian algebras such as M∞ may be expected to be of direct relevance to string theory. W
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18

Bektaş, Özcan, and Süleyman Şenyurt. "On Some Characterizations of Ruled Surface of a Closed Timelike Curve in Dual Lorentzian Space." Advances in Applied Clifford Algebras 22, no. 4 (2012): 939–53. http://dx.doi.org/10.1007/s00006-012-0327-7.

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19

Makki, Roa. "Some characterizations of non-null rectifying curves in dual Lorentzian 3-space $\mathbb{D}_{1}^{3}$." AIMS Mathematics 6, no. 3 (2021): 2114–31. http://dx.doi.org/10.3934/math.2021129.

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20

Ayyildiz, Nihat, and Ahmet Yucesan. "ON THE SCALAR AND DUAL FORMULATIONS OF THE CURVATURE THEORY OF LINE TRAJECTORIES IN THE LORENTZIAN SPACE." Journal of the Korean Mathematical Society 43, no. 6 (2006): 1339–55. http://dx.doi.org/10.4134/jkms.2006.43.6.1339.

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21

Andrejic, Vladica. "On Lorentzian spaces of constant sectional curvature." Publications de l'Institut Math?matique (Belgrade) 103, no. 117 (2018): 7–15. http://dx.doi.org/10.2298/pim1817007a.

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We investigate Osserman-like conditions for Lorentzian curvature tensors that imply constant sectional curvature. It is known that Osserman (moreover zwei-stein) Lorentzian manifolds have constant sectional curvature. We prove that some generalizations of the Rakic duality principle (Lorentzian totally Jacobi-dual or four-dimensional Lorentzian Jacobi-dual) imply constant sectional curvature. Moreover, any four-dimensional Jacobi-dual algebraic curvature tensor such that the Jacobi operator for some nonnull vector is diagonalizable, is Osserman. Additionally, any Lorentzian algebraic curvature
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22

Chudecki, Adam. "All ASD complex and real 4-dimensional Einstein spaces with Λ≠0 admitting a nonnull Killing vector". International Journal of Geometric Methods in Modern Physics 13, № 02 (2016): 1650011. http://dx.doi.org/10.1142/s0219887816500110.

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Anti-self-dual (ASD) 4-dimensional complex Einstein spaces with nonzero cosmological constant [Formula: see text] equipped with a nonnull Killing vector are considered. It is shown that any conformally nonflat metric of such spaces can be always brought to a special form and the Einstein field equations can be reduced to the Boyer–Finley–Plebański equation (Toda field equation). Some alternative forms of the metric are discussed. All possible real slices (neutral, Euclidean and Lorentzian) of ASD complex Einstein spaces with [Formula: see text] admitting a nonnull Killing vector are found.
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23

Naghi, Monia F., Rashad A. Abdel-Baky, and Fatemah Mofarreh. "Time-like Ruled Surface in One-Parameter Hyperbolic Dual Spherical Motions." Abstract and Applied Analysis 2022 (January 17, 2022): 1–10. http://dx.doi.org/10.1155/2022/9323490.

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In this work, we introduce a time-like ruled surface in one-parameter hyperbolic dual spherical motions. This provides the ability to derive some formulae of surface theory into line spaces. Then, a time-like Plücker conoid associated with the motion has been obtained, and its kinematic geometry is researched in detail. Consequently, a characterization for a time-like ruled surface to be a constant Disteli-axis is derived and investigated in detail. At last, we have discussed some special cases which lead to some special time-like ruled surfaces such as the time-like helicoids, Lorentzian sphe
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24

Talat, KORPINAR, and TURHAN Essin. "Dual Spacelike Elastic Biharmonic Curves with Timelike Principal Normal According to Dual Bishop Frames." November 15, 2011. https://doi.org/10.5281/zenodo.825553.

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In this paper, we study dual spacelike elastic biharmonic curves with spacelike binormal in dual Lorentzian space D<sup>3</sup><sub>1</sub>. We use Noether’s Theorem in our main theorem. Finally we obtain Killing vector field acoording to dual spacelike elastic biharmonic curves with spacelike binormal in dual Lorentzian space D<sup>3</sup><sub>1</sub>.
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25

Suha, Yılmaz, Unluturk Yasin, and Ziya Savcı Umit. "On Dual Curves of Constant Breadth According to Dual Bishop Frame in Dual Lorentzian Space D31." March 22, 2016. https://doi.org/10.5281/zenodo.815718.

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In this work, dual curves of constant breadth according to Bishop frame are defined, and applications of their differential equations are solved for special cases in dual Lorentzian space D<sup>3<sub>1</sub></sup>.
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26

Crawley, Erin, Alfredo Guevara, Noah Miller, and Andrew Strominger. "Black holes in Klein space." Journal of High Energy Physics 2022, no. 10 (2022). http://dx.doi.org/10.1007/jhep10(2022)135.

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Abstract The analytic continuation of the general signature (1, 3) Lorentzian Kerr-Taub-NUT black holes to signature (2, 2) Kleinian black holes is studied. Their global structure is characterized by a toric Penrose diagram resembling their Lorentzian counterparts. Kleinian black holes are found to be self-dual when their mass and NUT charge are equal for any value of the Kerr rotation parameter a. Remarkably, it is shown that the rotation a can be eliminated by a large diffeomorphism; this result also holds in Euclidean signature. The continuation from Lorentzian to Kleinian signature is natu
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27

Ozcan, BEKTAS, and SENYURT Suleyman. "On Some Characterization of Ruled Surface of a Closed Spacelike Curve with Spacelike Binormal in Dual Lorentzian Space." July 30, 2013. https://doi.org/10.5281/zenodo.824977.

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28

"Evolutes of Hyperbolic Dual Spherical Curve in Dual Lorentzian 3-Space." International Journal of Analysis and Applications, 2017. http://dx.doi.org/10.28924/2291-8639-15-2017-114.

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29

Emin, Özyılmaz. "On the Determination of a Time-like Dual Curve in Dual Lorentzian Space." November 22, 2009. https://doi.org/10.5281/zenodo.1084964.

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In this work, position vector of a time-like dual curve according to standard frame of D31 is investigated. First, it is proven that position vector of a time-like dual curve satisfies a dual vector differential equation of fourth order. The general solution of this dual vector differential equation has not yet been found. Due to this, in terms of special solutions, position vectors of some special time-like dual curves with respect to standard frame of D31 are presented.
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30

Çarboğa, Mert, and Yusuf Yaylı. "Geometry of Umbrella Matrices in Lorentz Space." Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, March 27, 2025. https://doi.org/10.1007/s40010-025-00918-x.

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Abstract In this study, umbrella matrices in Lorentz space are examined for the first time in the context of Lie groups and Lie algebra. The relationship between the Euclidean and Lorentz Umbrella Lie groups is presented through a different approach, and a new dual transformation is defined between their Lie Algebra. In addition, the characterization of double-umbrella matrices is obtained using a different Lorentzian metric.
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31

Anninos, Dionysios, Damian Galante, and Beatrix Mühlmann. "Finite Features of Quantum De Sitter Space." Classical and Quantum Gravity, December 14, 2022. http://dx.doi.org/10.1088/1361-6382/acaba5.

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Abstract We consider degrees of freedom for a quantum de Sitter spacetime. The problem is studied from both a Lorentzian and a Euclidean perspective. From a Lorentzian perspective, we compute dynamical properties of the static patch de Sitter horizon. These are compared to dynamical features of a black hole. We point out differences suggestive of non-standard thermal behaviour for the de Sitter horizon. We establish that geometries interpolating between an asymptotically AdS2×S2 space and a dS4 interior are compatible with the null energy condition, albeit with a non-standard decreasing radial
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32

Yapar, Z., and Y. Sa\u{g}iro\u{g}lu. "ON THE GEOMETRY OF CLOSED TIMELIKE RULED SURFACES IN DUAL LORENTZIAN SPACE." International Journal of Apllied Mathematics 29, no. 1 (2016). http://dx.doi.org/10.12732/ijam.v29i1.2.

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33

Bu, Wei, and Sean Seet. "A hidden 2d CFT for self-dual Yang-Mills on the celestial sphere." Journal of High Energy Physics 2024, no. 8 (2024). http://dx.doi.org/10.1007/jhep08(2024)022.

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Abstract Self-dual Yang-Mills theory admits an underlying infinite dimensional symmetry algebra, which has been obtained from mode expansion of Mellin transformed 4d scattering amplitudes and separately, Koszul duality on twistor space. In this paper, we propose to derive an explicit 2d realization of the algebra by performing a particular gauge transformation on the twistor action for self-dual Yang-Mills. The gauge parameter used in the transformation generates pure gauge connections corresponding to large gauge transformations on 4d Minkowski space, which localises part of the twistor actio
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34

Meltzer, David, and Allic Sivaramakrishnan. "CFT unitarity and the AdS Cutkosky rules." Journal of High Energy Physics 2020, no. 11 (2020). http://dx.doi.org/10.1007/jhep11(2020)073.

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Abstract We derive the Cutkosky rules for conformal field theories (CFTs) at weak and strong coupling. These rules give a simple, diagrammatic method to compute the double-commutator that appears in the Lorentzian inversion formula. We first revisit weakly-coupled CFTs in flat space, where the cuts are performed on Feynman diagrams. We then generalize these rules to strongly-coupled holographic CFTs, where the cuts are performed on the Witten diagrams of the dual theory. In both cases, Cutkosky rules factorize loop diagrams into on-shell sub-diagrams and generalize the standard S-matrix cuttin
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35

Singh, Ranveer Kumar, and Madhav Sinha. "Non-chiral vertex operator algebra associated to Lorentzian lattices and Narain CFTs." SciPost Physics 17, no. 2 (2024). http://dx.doi.org/10.21468/scipostphys.17.2.047.

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Frenkel, Lepowsky, and Meurman constructed a vertex operator algebra (VOA) associated to any even, integral, Euclidean lattice. In the language of physics, these are examples of chiral conformal field theories (CFT). In this paper, we define non-chiral vertex operator algebra and some associated notions. We then give a construction of a non-chiral VOA associated to an even, integral, Lorentzian lattice and construct their irreducible modules. We obtain the moduli space of such modular invariant non-chiral CFTs based on even, self-dual Lorentzian lattices of signature (m,n)(m,n) assuming the va
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36

Reeves, Wyatt, Moshe Rozali, Petar Simidzija, James Sully, Christopher Waddell, and David Wakeham. "Looking for (and not finding) a bulk brane." Journal of High Energy Physics 2021, no. 12 (2021). http://dx.doi.org/10.1007/jhep12(2021)002.

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Abstract When does a holographic CFT with a boundary added to it (a BCFT) also have a ‘good’ holographic dual with a localized gravitating end-of-the-world brane? We argue that the answer to this question is almost never. By studying Lorentzian BCFT correlators, we characterize constraints imposed on a BCFT by the existence of a bulk causal structure. We argue that approximate ‘bulk brane’ singularities place restrictive constraints on the spectrum of a BCFT that are not expected to be true generically. We discuss how similar constraints implied by bulk causality might apply in higher-dimensio
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37

Alday, Luis F., Maria Nocchi, Romain Ruzziconi, and Akshay Yelleshpur Srikant. "Carrollian amplitudes from holographic correlators." Journal of High Energy Physics 2025, no. 3 (2025). https://doi.org/10.1007/jhep03(2025)158.

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Abstract Carrollian amplitudes are flat space amplitudes written in position space at null infinity which can be re-interpreted as correlators in a putative dual Carrollian CFT. We argue that these amplitudes are the natural objects obtained in the flat space limit of AdS Lorentzian boundary correlators. The flat limit is taken entirely in position space by introducing Bondi coordinates in the bulk. From the bulk perspective, this procedure makes it manifest that the flat limit of any Witten diagram is the corresponding flat space Feynman diagram. It also makes explicit the fact that the flat
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38

Huang, Zhongjie, Bo Wang, Ellis Ye Yuan, and Xinan Zhou. "AdS super gluon scattering up to two loops: a position space approach." Journal of High Energy Physics 2023, no. 7 (2023). http://dx.doi.org/10.1007/jhep07(2023)053.

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Abstract We carry out a bootstrap study of four-point correlators in 4d $$ \mathcal{N} $$ N = 2 SCFTs which are dual to super Yang-Mills on AdS5 × S3. We focus on the simplest $$ \frac{1}{2} $$ 1 2 -BPS operators which correspond to the super gluons in the massless current multiplet. Our computation is based on an ansatz in position space which is inspired by a hidden symmetry structure manifest in the leading terms of the Lorentzian singularities of the correlators. By using other consistency conditions, we completely fix the super gluon correlators at one and two loops in the bulk genus expa
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39

Zolfi, Hamed. "Complexity and Multi-boundary Wormholes in 2 + 1 dimensions." Journal of High Energy Physics 2023, no. 4 (2023). http://dx.doi.org/10.1007/jhep04(2023)076.

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Abstract Three dimensional wormholes are global solutions of Einstein-Hilbert action. These space-times which are quotients of a part of global AdS3 have multiple asymptotic regions, each with conformal boundary S1 × ℝ, and separated from each other by horizons. Each outer region is isometric to BTZ black hole, and behind the horizons, there is a complicated topology. The main virtue of these geometries is that they are dual to known CFT states. In this paper, we evaluate the full time dependence of holographic complexity for the simplest case of 2 + 1 dimensional Lorentzian wormhole spacetime
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40

Alday, Luis F., Shai M. Chester, and Himanshu Raj. "ABJM at strong coupling from M-theory, localization, and Lorentzian inversion." Journal of High Energy Physics 2022, no. 2 (2022). http://dx.doi.org/10.1007/jhep02(2022)005.

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Abstract We study the stress tensor multiplet four-point function in the 3d maximally supersymmetric ABJ(M) theory with Chern-Simons level k = 2, which in the large N limit is holographically dual to weakly coupled M-theory on AdS4 × S7/ℤ2. We use the Lorentzian inversion to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity R and the first higher derivative correction R4 vertices, up to a finite number of contact terms that contribute to low spins where the inversion formula does not converge. We find a precise match with the correspondi
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41

Durka, Remigiusz. "The first law of black hole thermodynamics for Taub–NUT spacetime." International Journal of Modern Physics D 31, no. 04 (2022). http://dx.doi.org/10.1142/s0218271822500213.

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This paper focuses on the new approach to the nature of a nut parameter [Formula: see text], usually treated as a dual charge to the mass. Instead of thinking about it as a gravitational analog of the magnetic monopole, we will show that the Taub–NUT spacetime conceals a peculiar rotation coming from the Misner strings depending on the nut value. Besides reconciling several confusing results present in the literature, this allows us to establish more the less a consistent description of the black hole thermodynamics for the Lorentzian Taub–NUT spacetime with essential contribution from the Mis
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42

Blommaert, Andreas, Thomas G. Mertens, and Jacopo Papalini. "The dilaton gravity hologram of double-scaled SYK." Journal of High Energy Physics 2025, no. 6 (2025). https://doi.org/10.1007/jhep06(2025)050.

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Abstract We work out a precise holographic duality between sine dilaton gravity, and DSSYK. More precisely, canonical quantization of sine dilaton gravity reproduces q-Schwarzian quantum mechanics, which is the auxiliary system that arises from the chord diagrams of DSSYK. The role of the chord number in DSSYK is played by the (Weyl rescaled) geodesic length in the bulk. The most puzzling aspect of reconciling DSSYK with a simple gravitational dual at the classical level is the distinction between temperature and “fake temperature”. At the q-Schwarzian level, we clarify how this arises from th
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43

Özdemir, Zehra, Şirin Gonca Perçin, and Hazal Ceyhan. "Propagation of the polarized light along an optical fiber via Rodrigues formula and Lorentzian screw motion." Physica Scripta, January 3, 2025. https://doi.org/10.1088/1402-4896/ada590.

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Abstract In this study, we investigate the propagation of polarized light along an optical fiber with the help of screw motion and Clifford's algebra of hyperbolic split dual quaternion in $\mathbb{R}^{1,2}_{\sigma_{1},\sigma_{2},\sigma_{3}}$. The importance of this study is to hyperbolic screw motion allows to characterize four types of polarization states of polarized light waves in an optical fiber. These are elliptical polarization ((E)-polarization), circular polarization ((C)-polarization), Lorentzian circular polarization ((LC)-polarization), and linear polarization ((L)-polarization).
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44

Bobev, Nikolay, Anthony M. Charles, and Vincent S. Min. "Euclidean black saddles and AdS4 black holes." Journal of High Energy Physics 2020, no. 10 (2020). http://dx.doi.org/10.1007/jhep10(2020)073.

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Abstract We find new asymptotically locally AdS4 Euclidean supersymmetric solutions of the STU model in four-dimensional gauged supergravity. These “black saddles” have an S1×$$ {\Sigma}_{\mathfrak{g}} $$ Σ g boundary at asymptotic infinity and cap off smoothly in the interior. The solutions can be uplifted to eleven dimensions and are holographically dual to the topologically twisted ABJM theory on S1×$$ {\Sigma}_{\mathfrak{g}} $$ Σ g . We show explicitly that the on-shell action of the black saddle solutions agrees exactly with the topologically twisted index of the ABJM theory in the planar
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45

Van Raamsdonk, Mark. "Cosmology from confinement?" Journal of High Energy Physics 2022, no. 3 (2022). http://dx.doi.org/10.1007/jhep03(2022)039.

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Abstract We describe a class of holographic models that may describe the physics of certain four-dimensional big-bang/big-crunch cosmologies. The construction involves a pair of 3D Euclidean holographic CFTs each on a homogeneous and isotropic space M coupled at either end of an interval ℐ to a Euclidean 4D CFT on M × ℐ with many fewer local degrees of freedom. We argue that in some cases, when the size of M is much greater than the length of ℐ, the theory flows to a confining three-dimensional field theory on M in the infrared, and this is reflected in the dual description by the asymptotical
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46

Da Silva, Luiz C. B. "Rotation minimizing frames and spherical curves in simply isotropic and pseudo-isotropic 3-spaces." Tamkang Journal of Mathematics 51, no. 1 (2020). http://dx.doi.org/10.5556/j.tkjm.51.2020.2960.

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In this work, we are interested in the differential geometry of curves in the simply isotropic and pseudo-isotropic 3-spaces, which are examples of Cayley-Klein geometries whose absolute figure is given by a plane at infinity and a degenerate quadric. Motivated by the success of rotation minimizing (RM) frames in Euclidean and Lorentzian geometries, here we show how to build RM frames in isotropic geometries and apply them in the study of isotropic spherical curves. Indeed, through a convenient manipulation of osculating spheres described in terms of RM frames, we show that it is possible to c
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47

Chandra, A. Ramesh, Jan de Boer, Mario Flory, Michal P. Heller, Sergio Hörtner, and Andrew Rolph. "Cost of holographic path integrals." SciPost Physics 14, no. 4 (2023). http://dx.doi.org/10.21468/scipostphys.14.4.061.

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We consider proposals for the cost of holographic path integrals. Gravitational path integrals within finite radial cutoff surfaces have a precise map to path integrals in T\overline{T}TT¯ deformed holographic CFTs. In Nielsen’s geometric formulation cost is the length of a not-necessarily-geodesic path in a metric space of operators. Our cost proposals differ from holographic state complexity proposals in that (1) the boundary dual is cost, a quantity that can be 'optimised' to state complexity, (2) the set of proposals is large: all functions on all bulk subregions of any co-dimension which
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48

Caron-Huot, Simon, Dalimil Mazáč, Leonardo Rastelli, and David Simmons-Duffin. "Dispersive CFT sum rules." Journal of High Energy Physics 2021, no. 5 (2021). http://dx.doi.org/10.1007/jhep05(2021)243.

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Abstract We give a unified treatment of dispersive sum rules for four-point correlators in conformal field theory. We call a sum rule “dispersive” if it has double zeros at all double-twist operators above a fixed twist gap. Dispersive sum rules have their conceptual origin in Lorentzian kinematics and absorptive physics (the notion of double discontinuity). They have been discussed using three seemingly different methods: analytic functionals dual to double-twist operators, dispersion relations in position space, and dispersion relations in Mellin space. We show that these three approaches ca
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49

Sahu, Abhisek, and Mark Van Raamsdonk. "Holographic black hole cosmologies." Journal of High Energy Physics 2025, no. 5 (2025). https://doi.org/10.1007/jhep05(2025)233.

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Abstract We describe and study a holographic construction of big-bang / big-crunch cosmological spacetimes where the matter consists of a lattice of black holes. The cosmological spacetime is dual to an entangled state of a collection of holographic CFTs associated with the second asymptotic regions of the black holes. For a cosmology with spatial slice geometry Σ, this state is constructed via a Euclidean path integral for the CFT on a geometry obtained by connecting two copies of Σ by a lattice of tubes. In three-dimensional gravity, we describe the cosmological solutions and the associated
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50

Das, Suchetan. "Stretched horizon from conformal field theory." Journal of High Energy Physics 2024, no. 11 (2024). http://dx.doi.org/10.1007/jhep11(2024)033.

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Abstract Recently, it has been observed that the Hartle-Hawking correlators, a signature of smooth horizon, can emerge from certain heavy excited state correlators in the (manifestly non-smooth) BTZ stretched horizon background, in the limit when the stretched horizon approaches the real horizon. In this note, we develop a framework of quantizing the CFT modular Hamiltonian, that explains the necessity of introducing a stretched horizon and the emergence of thermal features in the AdS-Rindler and (planar) BTZ backgrounds. In more detail, we quantize vacuum modular Hamiltonian on a spatial segm
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