Level-rank duality of WZW models in conformal field theory
type: Item
instance of: scholarly article
title: Level-rank duality of WZW models in conformal field theory
zbMATH Open document ID: 0751.17024
DOI: 10.1007/BF02101097
author: Tomoki Nakanishi
author: Akihiro Tsuchiya
published in: Communications in Mathematical Physics
publication date: 1992-09-26T00:00:00Z
review text: The decomposition of the conformal blocks under the conformal embedding is considered. In addition to the known mutually commutative embedding of affine Lie algebras \(\widehat {sl}(l)_ r\times \widehat{sl}(r)_ l\subset\widehat{gl}(lr)_ 1\) (Frenkel, 1982), the case of \(\widehat {sl}(l)_ r\times\widehat{sl}(r)_ l\times \hat a\subset gl(lr)_ 1\) where \(\hat a\) is an affine extension of the abelian subalgebra of central elements of \(gl(lr)\), is studied in detail. It is shown that a pairing between the spaces of conformal blocks of \(\widehat{sl}(l)_ r\) and \(\widehat{sl}(r)_ l\) Wess-Zumino-Witten models on the Riemann sphere (Witten, 1984; Knizhnik-Zamolodchikov, 1984) which is induced by the reciprocal decompositions of \(\widehat{gl}(lr)_ 1\)-modules and satisfies the completeness condition, defines the level-rank duality [\textit{S. G. Naculich} and \textit{H. J. Schnitzer}, Phys. Lett. 244, No. 2, 235-240 (1990); Nucl. Phys. B 347, No. 3, 687-742 (1990)]\ between two spaces in conformal field theory under consideration.
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 54750
zbMATH Keywords: affine Lie algebras
zbMATH Keywords: conformal blocks
zbMATH Keywords: Wess-Zumino-Witten models
zbMATH Keywords: level- rank duality
zbMATH Keywords: conformal field theory
reviewed by: A. A. Bogush
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02101097
OpenAlex ID: W2004585753
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description: scientific article; zbMATH DE number 54750