From Integrable Models to Conformal Field Theory Via Quantum Groups

1993 ◽  
pp. 1-24 ◽  
Author(s):  
L. D. Faddeev
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Groups ◽  
Integrable Models ◽  
Conformal Field

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.

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.

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