Current algebras and Wess-Zumino model in two dimensions. (English) Zbl 0661.17020

We investigate quantum field theory in two dimensions invariant with respect to conformal (Virasoro) and non-abelian current (Kac-Moody) algebras. The Wess-Zumino model is related to the special case of the representations of these algebras, the conformal generators being quadratically expressed in terms of currents. The anomalous dimensions of the Wess-Zumino fields are found exactly, and the multipoint correlation functions are shown to satisfy linear differential equations. In particular, Witten’s non-abelian bosonisation rules are proven.


17B65 Infinite-dimensional Lie (super)algebras
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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