scholarly journals A guide to two-dimensional conformal field theory

2019 ◽  
pp. 60-120
Author(s):  
Jörg Teschner
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Virasoro Algebra ◽  
Integrable Models ◽  
Two Dimensional ◽  
Isomonodromic Deformation ◽  
Conformal Field ◽  
Deformation Problem ◽  
Basic Formalism ◽  
Higher Genus

This is a review of two-dimensional conformal field theory including the Virasoro algebra, the bootstrap, and some of the relations to integrable models. An effort is made to develop the basic formalism in a way which is both elementary but also as flexible as possible at the same time. Some advanced topics such as conformal field theory on higher genus surfaces and relations to the isomonodromic deformation problem are discussed; for other topics we offer a first guide to the literature.

CORRELATORS OF CONFORMAL FIELD THEORIES FROM THEIR CHARACTERS

1990 ◽  
Vol 05 (31) ◽  
pp. 2643-2649
Author(s):  
R. P. MALIK ◽  
N. BEHERA ◽  
R. K. KAUL
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Complete Solution ◽  
Arbitrary Point ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Genus

All genus characters define a complete solution of a two-dimensional rational conformal field theory. An arbitrary point correlator can be obtained by an appropriate combination of the pinchings of zero-homology and non-zero-homology cycles of the characters on the higher genus Riemann surface.

scholarly journals Analysis for Lorentzian conformal field theories through sine-square deformation

2020 ◽  
Vol 2020 (6) ◽  
Author(s):  
Xun Liu ◽  
Tsukasa Tada
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Continuous Spectrum ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
The Third

Abstract We reexamine two-dimensional Lorentzian conformal field theory using the formalism previously developed in a study of sine-square deformation of Euclidean conformal field theory. We construct three types of Virasoro algebra. One of them reproduces the result by Lüscher and Mack, while another type exhibits divergence in the central charge term. The third leads to a continuous spectrum and contains no closed time-like curve in the system.

scholarly journals Notes on Curtright–Zachos Deformations of osp(1,2) and Super Virasoro Algebras

1997 ◽  
Vol 12 (32) ◽  
pp. 5867-5883
Author(s):  
Naruhiko Aizawa ◽  
Tatsuo Kobayashi ◽  
Haru-Tada Sato
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
String Theory ◽  
Virasoro Algebra ◽  
Two Dimensional ◽  
Supersymmetric Extension ◽  
Conformal Field ◽  
Deformed Algebra ◽  
Deformed Virasoro Algebra

Based on the quantum superspace construction of q-deformed algebra, we discuss a supersymmetric extension of the deformed Virasoro algebra, which is a subset of the q–W∞ algebra which recently appeared in the context of two-dimensional string theory. We analyze two types of deformed super Virasoro algebra as well as their osp(1,2) subalgebras. Applying our quantum superspace structure to conformal field theory, we find the same type of deformation of affine sl(2) algebra.

A Review of Conformal Field Theory in 2D

2014 ◽  
Vol 6 (2) ◽  
pp. 1079-1105
Author(s):  
Rahul Nigam
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Conformal Field Theory ◽  
Statistical Mechanics ◽  
Critical Behavior ◽  
Verma Module ◽  
Virasoro Algebra ◽  
Quantum Field ◽  
Conformal Field ◽  
Insight Into

In this review we study the elementary structure of Conformal Field Theory in which is a recipe for further studies of critical behavior of various systems in statistical mechanics and quantum field theory. We briefly review CFT in dimensions which plays a prominent role for example in the well-known duality AdS/CFT in string theory where the CFT lives on the AdS boundary. We also describe the mapping of the theory from the cylinder to a complex plane which will help us gain an insight into the process of radial quantization and radial ordering. Finally we will develop the representation of the Virasoro algebra which is the well-known "Verma module".  

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.

POISSON–LIE GROUPS AND CLASSICAL W-ALGEBRAS

1992 ◽  
Vol 07 (05) ◽  
pp. 853-876 ◽  
Author(s):  
V. A. FATEEV ◽  
S. L. LUKYANOV
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Group ◽  
Lie Groups ◽  
Group Structure ◽  
Two Dimensional ◽  
Poisson Structures ◽  
Additional Symmetries ◽  
Conformal Field ◽  
Poisson Lie Groups

This is the first part of a paper studying the quantum group structure of two-dimensional conformal field theory with additional symmetries. We discuss the properties of the Poisson structures possessing classical W-invariance. The Darboux variables for these Poisson structures are constructed.

scholarly journals SU(2)k×SU(2)l/SU(2)k+l COSET CONFORMAL FIELD THEORY AND TOPOLOGICAL MINIMAL MODEL ON HIGHER GENUS RIEMANN SURFACE

1993 ◽  
Vol 08 (31) ◽  
pp. 5537-5561 ◽  
Author(s):  
HITOSHI KONNO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Vertex Operator ◽  
Correlation Functions ◽  
Minimal Model ◽  
The Other ◽  
Operator Formalism ◽  
Conformal Field ◽  
Higher Genus

We consider the Feigin-Fuchs-Felder formalism of the SU (2)k× SU (2)l/ SU (2)k+l coset minimal conformal field theory and extend it to higher genus. We investigate a double BRST complex with respect to two compatible BRST charges, one associated with the parafermion sector and the other associated with the minimal sector in the theory. The usual screened vertex operator is extended to the BRST-invariant screened three-string vertex. We carry out a sewing operation of these vertices and derive the BRST-invariant screened g-loop operator. The latter operator characterizes the higher genus structure of the theory. An analogous operator formalism for the topological minimal model is obtained as the limit l=0 of the coset theory. We give some calculations of correlation functions on higher genus.

scholarly journals ON THE CFT DUALS FOR NEAR-EXTREMAL BLACK HOLES

2011 ◽  
Vol 26 (22) ◽  
pp. 1601-1611 ◽  
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Field Theory ◽  
Black Holes ◽  
Black Hole ◽  
Conformal Field Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Horizon Geometry ◽  
Cardy Formula ◽  
Asymptotic Symmetries ◽  
Extremal Black Holes

We consider Kerr–Newman–AdS–dS black holes near extremality and work out the near-horizon geometry of these near-extremal black holes. We identify the exact U (1)L× U (1)R isometries of the near-horizon geometry and provide boundary conditions enhancing them to a pair of commuting Virasoro algebras. The conserved charges of the corresponding asymptotic symmetries are found to be well-defined and nonvanishing and to yield central charges cL≠0 and cR = 0. The Cardy formula subsequently reproduces the Bekenstein–Hawking entropy of the black hole. This suggests that the near-extremal Kerr–Newman–AdS–dS black hole is holographically dual to a non-chiral two-dimensional conformal field theory.

Sign in / Sign up

Export Citation Format

Share Document