Fjelstad, Jens On duality and extended chiral symmetry in the \(SL(2,\mathbb R)\) WZW model. (English) Zbl 1219.81212 J. Phys. A, Math. Theor. 44, No. 23, Article ID 235404, 29 p. (2011). 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. Cited in 3 Documents 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 PDFBibTeX XMLCite \textit{J. Fjelstad}, J. Phys. A, Math. Theor. 44, No. 23, Article ID 235404, 29 p. (2011; Zbl 1219.81212) Full Text: DOI arXiv