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 ${\mathrm{\phi }}_{\mathrm{GWZW}}$. 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 arbitary genus Riemann surface. As a by-product we discover a new way to explain the appearance of quantum groups in the WZW model. © 1995 The American Physical Society.

• Received 11 July 1995

DOI:https://doi.org/10.1103/PhysRevD.52.7146