Anton Yu. Alekseev, Peter Schaller, Thomas Strobl
The Topological G/G WZW Model in the Generalized Momentum Representation
Preprint series: ESI preprints

MSC:

81R50 Quantum groups and related algebraic methods, See Also {16W30, 17B37}

81T40 Two-dimensional field theories, conformal field theories, etc.

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 $\Psi(g)$ 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 appearence of
Quantum Groups in the WZW model.

Keywords: gauged WZW-model, chiral field, quantum group, sigma model