scholarly journals A class of Hermitian generalized Jordan triple systems and Chern–Simons gauge theory

2014 ◽  
Vol 29 (29) ◽  
pp. 1450156
Author(s):  
Noriaki Kamiya ◽  
Matsuo Sato
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Triple Systems ◽  
Fundamental Matter ◽  
Jordan Triple Systems ◽  
Chern Simons

We find a class of Hermitian generalized Jordan triple systems (HGJTSs) and Hermitian (ϵ, δ)-Freudenthal–Kantor triple systems (HFKTSs). We apply one of the most simple HGJTSs which we find to a field theory and obtain a typical u(N) Chern–Simons gauge theory with a fundamental matter.

Hermitian generalized Jordan triple systems and certain applications to field theory

2014 ◽  
Vol 29 (13) ◽  
pp. 1450071 ◽  
Author(s):  
Noriaki Kamiya ◽  
Matsuo Sato
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Triple System ◽  
Structure Theorem ◽  
Triple Systems ◽  
Jordan Triple System ◽  
Mathematical Properties ◽  
Jordan Triple Systems ◽  
Chern Simons

We define Hermitian generalized Jordan triple systems and prove a structure theorem. We also give some examples of the systems and study mathematical properties. We apply a Hermitian generalized Jordan triple system to a field theory and obtain a Chern–Simons gauge theory.

scholarly journals Hermitian(ϵ,δ)-Freudenthal-Kantor Triple Systems and Certain Applications of*-Generalized Jordan Triple Systems to Field Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Noriaki Kamiya ◽  
Matsuo Sato
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Triple System ◽  
Structure Theorem ◽  
Higgs Mechanism ◽  
The Novel ◽  
Yang Mills ◽  
Triple Systems ◽  
Jordan Triple Systems ◽  
Chern Simons

We define Hermitian(ϵ,δ)-Freudenthal-Kantor triple systems and prove a structure theorem. We also give some examples of triple systems that are generalizations of theu(N)⊕u(M)andsp(2N)⊕u(1)Hermitian 3-algebras. We apply a*-generalized Jordan triple system to a field theory and obtain a Chern-Simons gauge theory. We find that the novel Higgs mechanism works, where the Chern-Simons gauge theory reduces to a Yang-Mills theory in a certain limit.

scholarly journals PLANAR HOMOLOGICAL MIRROR SYMMETRY

2007 ◽  
Vol 22 (29) ◽  
pp. 5351-5368 ◽  
Author(s):  
EIJI KONISHI
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Associative Algebra ◽  
String Field Theory ◽  
Mirror Symmetry ◽  
Open String ◽  
Homological Mirror Symmetry ◽  
Chern Simons

In this paper, we formulate a planar limited version of the B-side in homological mirror symmetry that formularizes Chern–Simons-type topological open string field theory using homotopy associative algebra (A∞ algebra). This formulation is based on the works by Dijkgraaf and Vafa. We show that our formularization includes gravity/gauge theory correspondence which originates in the AdS/CFT duality of Dijkgraaf–Vafa theory.

O(2) CHERN–SIMONS GAUGE THEORY AND Z2 ORBIFOLDS

1992 ◽  
Vol 07 (05) ◽  
pp. 1007-1023 ◽  
Author(s):  
KAORU AMANO ◽  
HIROSHI SHIROKURA
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Coherent State ◽  
Gauge Field ◽  
Three Dimensional ◽  
The State ◽  
Explicit Calculation ◽  
Gauge Field Theory ◽  
State Representation ◽  
Chern Simons

We quantize the three-dimensional O(2) pure Chern–Simons gauge field theory in a functional coherent-state representation. Both trivial and nontrivial flat O(2) bundles admit physical states. An explicit calculation relates the state functionals to the rational Z2-orbifold models.

Integrability: From Statistical Systems to Gauge Theory

2019 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Summer School ◽  
Condensed Matter ◽  
Theoretical Physics ◽  
Conformal Field ◽  
The Past ◽  
Background Material ◽  
Supersymmetric Gauge ◽  
Statistical Systems

This volume contains lectures delivered at the Les Houches Summer School ‘Integrability: from statistical systems to gauge theory’ held in June 2016. The School was focussed on applications of integrability to supersymmetric gauge and string theory, a subject of high and increasing interest in the mathematical and theoretical physics communities over the past decade. Relevant background material was also covered, with lecture series introducing the main concepts and techniques relevant to modern approaches to integrability, conformal field theory, scattering amplitudes, and gauge/string duality. The book will be useful not only to those working directly on integrablility in string and guage theories, but also to researchers in related areas of condensed matter physics and statistical mechanics.

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

scholarly journals Extremal correlators and random matrix theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Alba Grassi ◽  
Zohar Komargodski ◽  
Luigi Tizzano
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Matrix Model ◽  
Effective Field Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Matrix Theory ◽  
Effective Field ◽  
Random Matrix Model ◽  
Large Charge

Abstract We study the correlation functions of Coulomb branch operators of four-dimensional $$ \mathcal{N} $$ N = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals Chern-Simons gravity dual of BCFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Tadashi Takayanagi ◽  
Takahiro Uetoko
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Entanglement Entropy ◽  
Einstein Gravity ◽  
Conformal Field ◽  
Holographic Entanglement Entropy ◽  
The World ◽  
Higher Spin ◽  
End Of The World ◽  
Chern Simons

Abstract In this paper we provide a Chern-Simons gravity dual of a two dimensional conformal field theory on a manifold with boundaries, so called boundary conformal field theory (BCFT). We determine the correct boundary action on the end of the world brane in the Chern-Simons gauge theory. This reproduces known results of the AdS/BCFT for the Einstein gravity. We also give a prescription of calculating holographic entanglement entropy by employing Wilson lines which extend from the AdS boundary to the end of the world brane. We also discuss a higher spin extension of our formulation.

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