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On duality and extended chiral symmetry in the \(SL(2,\mathbb R)\) WZW model. (English) Zbl 1219.81212

Summary: Two chiral aspects of the \(SL(2,\mathbb R)\) WZW model in an operator formalism are investigated. First, the meaning of duality, or conjugation, of primary fields is clarified. On a class of modules obtained from the discrete series it is shown, by looking at spaces of two-point conformal blocks, that a natural definition of contragredient module provides a suitable notion of conjugation of primary fields, consistent with known two-point functions. We find strong indications that an apparent contradiction with the Clebsch-Gordan series of \(SL(2,\mathbb R)\), and proposed fusion rules, is explained by non-semi-simplicity of a certain category. Second, results indicating an infinite cyclic simple current group, corresponding to spectral flow automorphisms, are presented. In particular, the subgroup corresponding to even spectral flow provides part of a hypothetical extended chiral algebra resulting in proposed modular invariant bulk spectra.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
22E70 Applications of Lie groups to the sciences; explicit representations
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