Level rank duality of WZW models in conformal field theory - INSPIRE

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Level rank duality of WZW models in conformal field theory

Jul, 1990

35 pages

Published in:

Commun.Math.Phys. 144 (1992) 351-372

DOI:

10.1007/BF02101097

Report number:

NU-MATH-002

reference search73 citations

Citations per year

Abstract: (Springer)

We consider the decomposition of the conformal blocks under the conformal embeddings. The case

\widehat{gl}\left( {lr} \right)_1\supset \widehat{sl}\left( l \right)_r\times \widehat{sl}\left( r \right)_l\times \hat a

(â is an affine extension of the abelian subalgebra of the central elements ofgl(lr)) is studied in detal. The reciprocal decompositions of

\widehat{gl}\left( {lr} \right)_1

-modules induce a pairing between the spaces of conformal blocks of

\widehat{sl}\left( l \right)_r

and

\widehat{sl}\left( r \right)_l

Wess-Zumino-Witten models on the Riemann sphere. The completeness of the pairing is shown. Hence it defines aduality between two spaces.

field theory: conformal
dimension: 2
Wess-Zumino-Witten model
algebra: Lie
algebra: affine
Riemann surface
duality

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