Comments on rational conformal field theory, quantum groups and tower of algebras

2008 ◽  
pp. 278-306
Author(s):  
César Gómez
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Groups ◽  
Conformal Field ◽  
Tower Of Algebras

scholarly journals SCREENING CURRENT REPRESENTATION OF QUANTUM SUPERALGEBRAS

1998 ◽  
Vol 13 (18) ◽  
pp. 1485-1493
Author(s):  
JØRGEN RASMUSSEN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Groups ◽  
Conformal Field ◽  
Contour Representation ◽  
Current Representation ◽  
Quantum Superalgebras

In this letter a screening current or contour representation is given for certain quantum superalgebras. The Gomez–Sierra construction of quantum groups in conformal field theory is generalized to cover superalgebras and illustrated using recent results on screening currents in affine current superalgebra.

RESHETIKHIN-TURAEV AND CRANE-KOHNO-KONTSEVICH 3-MANIFOLD INVARIANTS COINCIDE

1993 ◽  
Vol 02 (01) ◽  
pp. 65-95 ◽  
Author(s):  
SERGEY PIUNIKHIN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Explicit Formula ◽  
Quantum Groups ◽  
Jones Polynomial ◽  
Matrix Elements ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Wznw Model ◽  
The Matrix

The coincidence of two different presentations of Witten 3-manifold invariants is proved. One of them, invented by Reshetikhin and Turaev, is based on the surgery presentation a of 3-manifold and the representation theory of quantum groups; another one, invented by Kohno and Crane and, in slightly different language by Kontsevich, is based on a Heegaard decomposition of a 3-manifold and representations of the Teichmuller group, arising in conformal field theory. The explicit formula for the matrix elements of generators of the Teichmuller group in the space of conformal blocks in the SU(2) k, WZNW-model is given,using the Jones polynomial of certain links.

DEGENERATE AFFINE HECKE ALGEBRAS AND TWO-DIMENSIONAL PARTICLES

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 109-140 ◽  
Author(s):  
IVAN CHEREDNIK
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Quantum Groups ◽  
Hecke Algebras ◽  
Two Dimensional ◽  
Conformal Field ◽  
Affine Hecke Algebras ◽  
The Difference ◽  
Zamolodchikov Equation

We demonstrate that the quantization of momenta in different two dimensional theories of elementary particles with factorizable scattering amplitudes gives the so-called degenerate affine Hecke algebras and their versions. Some connections with quantum groups(Yangians), the two-dimensional conformal field theory and representation theory am discussed. In particular, an interpretation and generalizations of the difference counterpart of the Knizhnik-Zamolodchikov equation are found by means of the particles on a segment.

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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