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

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

1995-05-02

arxiv.org/abs/hep-th/9505012v2

Phys.Rev. D52 (1995) 7146-7160

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, LaTeX

Scientific paper

10.1103/PhysRevD.52.7146

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 $\Psi(g)$ is governed by a new gauge cocycle $\phi_{GWZW}$. We evaluate this cocycle explicitly using the machinery of Poisson $\sigma$-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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