G/G gauged WZW model and Bethe Ansatz for the phase model

TL;DR

This paper connects the G/G gauged WZW model on Riemann surfaces with the phase model's Bethe Ansatz, revealing a deep relationship between gauge theories and integrable models through localization and partition function analysis.

Contribution

It demonstrates how the G/G gauged WZW model's partition function can be expressed via Bethe Ansatz solutions of the phase model, establishing a novel link between gauge theory and integrable systems.

Findings

Partition function expressed as sum over Bethe Ansatz eigenstates.

Localization leads to Bethe Ansatz equations for the phase model.

Relations established between Chern-Simons theory and the phase model.

Abstract

We investigate the G/G gauged Wess-Zumino-Witten model on a Riemann surface from the point of view of the algebraic Bethe Ansatz for the phase model. After localization procedure is applied to the G/G gauged Wess-Zumino-Witten model, the diagonal components for group elements satisfy Bethe Ansatz equations for the phase model. We show that the partition function of the G/G gauged Wess-Zumino-Witten model is identified as the summation of norms with respect to all the eigenstates of the Hamiltonian with the fixed number of particles in the phase model. We also consider relations between the Chern-Simons theory on $S^1\times\Sigma_h$ and the phase model.