Abstract
We consider the Wess-Zumino-Witten two-dimensional sigma models with fields taking values in an arbitrary connected (but not necessarily simply connected) simple Lie groupG. The quantum states of the theory are realized geometrically as sections of a line bundle over the loop groupLG. The action of the current algebra of the theory is decomposed into highest weight representations by explicit construction of the highest weight states. This solves for the spectrum of the models. As a by-product, we obtain modular invariant partition functions of the theory on tori. The present paper extends the results of [7] where the casesG=SU(2) andSO(3) were treated.
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Communicated by A. Jaffe
Ce rapport a été publié en partie grâce à une subvention du Fonds FCAR pour l'aide et le soutien à la rercherche
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Felder, G., Gawedzki, K. & Kupiainen, A. Spectra of Wess-Zumino-Witten models with arbitrary simple groups. Commun.Math. Phys. 117, 127–158 (1988). https://doi.org/10.1007/BF01228414
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DOI: https://doi.org/10.1007/BF01228414