An Introduction to Integrable Models and Conformal Field Theory

1990 ◽  
pp. 1-30 ◽  
Author(s):  
H. Grosse
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Integrable Models ◽  
Conformal Field

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.

scholarly journals NONSTANDARD MATRIX FORMATS OF LIE SUPERALGEBRAS

1999 ◽  
Vol 14 (25) ◽  
pp. 4043-4060 ◽  
Author(s):  
F. DELDUC ◽  
F. GIERES ◽  
S. GOURMELEN ◽  
S. THEISEN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Groups ◽  
Systematic Study ◽  
Lie Superalgebras ◽  
Integrable Models ◽  
Standard Format ◽  
Conformal Field

The standard format of matrices belonging to Lie superalgebras consists of partitioning the matrices into even and odd blocks. In this paper, we present a systematic study of other possible matrix formats and in particular of the so-called diagonal format which naturally occurs in various physical applications, e.g. for the supersymmetric versions of conformal field theory, integrable models. W algebras and quantum groups.

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".  

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