SL(N) Kac-Moody algebras and Wess-Zumino-Witten models

Journal Article · Fri Mar 01 04:00:00 EST 1991 · Annals of Physics (New York); (United States)

DOI:https://doi.org/10.1016/0003-4916(91)90005-S· OSTI ID:5614797

Ruehl, W ^[1]

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1. Univ. Kaiserslautern (West Germany)

Wess-Zumino-Witten models are conformal invariant versions of two-dimensional {sigma}-models. In this article currents were defined properly from the principal field variable (the group valued field) of the {sigma}-model and their quantum commutators were proved to form a Kac-Moody algebra. Since then representation theory of Kac-Moody algebras and the Wess-Zumino-Witten (WZW) models have remained closely linked. Shortly after Knizhnik and Zamolochikov discovered a kind of first-order differential equations which enabled them to derive four-point functions of SU(N) {times} SU(N) models for particular representations and arbitrary value k. These equations played an important role in later research but will not be used by us.

• OSTI ID: 5614797
• Journal Information: Annals of Physics (New York); (United States), Journal Name: Annals of Physics (New York); (United States) Vol. 206:2; ISSN APNYA; ISSN 0003-4916
• Country of Publication: United States
• Language: English

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