Quasi-Hamiltonian bookkeeping of WZNW defects

TL;DR

This paper interprets the chiral WZNW model with monodromy as a quasi-Hamiltonian system, simplifying the understanding of symplectic structures in WZNW defects and moduli spaces of flat connections.

Contribution

It provides a novel quasi-Hamiltonian framework to explain symplectic structures of WZNW defects and moduli spaces, unifying complex cross-terms through fusion concepts.

Findings

Unified quasi-Hamiltonian description of WZNW defects

Simplified symplectic structure characterization of moduli spaces

Clarified the role of fusion in symplectic geometry

Abstract

We interpret the chiral WZNW model with general monodromy as an infinite dimensional quasi-Hamiltonian dynamical system. This interpretation permits to explain the totality of complicated cross-terms in the symplectic structures of various WZNW defects solely in terms of the single concept of the quasi-Hamiltonian fusion. Translated from the WZNW language into that of the moduli space of flat connections on Riemann surfaces, our result gives a compact and transparent characterisation of the symplectic structure of the moduli space of flat connections on a surface with k handles, n boundaries and m Wilson lines.