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The Topological G/G WZW Model in the Generalized Momentum Representation

A. Yu. Alekseev·P. Schaller·T. Strobl
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Abstract

We consider the topological gauged WZW model in the generalized momentum representation. The chiral field $g$ is interpreted as a counterpart of the electric field $E$ of conventional gauge theories. The gauge dependence of wave functionals $Ψ(g)$ is governed by a new gauge cocycle $ϕ_{GWZW}$. We evaluate this cocycle explicitly using the machinery of Poisson $σ$-models. In this approach the GWZW model is reformulated as a Schwarz type topological theory so that the action does not depend on the world-sheet metric. The equivalence of this new formulation to the original one is proved for genus one and conjectured for an arbitrary genus Riemann surface. As a by-product we discover a new way to explain the appearance of Quantum Groups in the WZW model.

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A. Yu. Alekseev, P. Schaller, T. Strobl. 1995-05-23. The Topological G/G WZW Model in the Generalized Momentum Representation. https://doi.org/10.1103/physrevd.52.7146

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