Integrability in Hamiltonian Chern-Simons theory

TL;DR

This paper introduces an integrable model based on the moduli space of flat connections in Hamiltonian Chern-Simons theory, revealing a gauge equivalence to the XXZ magnetic chain and providing a new parametrization for analysis.

Contribution

It presents a novel parametrization of the moduli space and constructs an integrable model with commuting Hamiltonians derived from Wilson line observables.

Findings

Constructed an integrable model on the moduli space.

Identified a family of commuting Hamiltonians from Wilson lines.

Showed gauge equivalence to the XXZ magnetic chain.

Abstract

We consider the moduli space of flat connections on the Riemann surface with marked points. The new efficient parametrization is suggested and used to construct an integrable model on the moduli space. A family of commuting Hamiltonians is extracted from the trace of the transfer matrix built from the Wilson line observables of the Chern-Simons theory. Our model appears to be gauge equivalent to XXZ magnetic chain with finite number of sites.