qQCD$_2$ and G/G model

TL;DR

This paper explores the relationship between a 2D lattice gauge theory with a quantum gauge group and the G/G coset model, revealing a duality despite their non-equivalence.

Contribution

It demonstrates a duality between the qQCD$_2$ model with quantum gauge group and the G/G coset model, highlighting their coinciding partition functions at specific parameters.

Findings

Partition functions coincide at specific q values

Models are dual but not equivalent

Reveals a new duality in 2D gauge theories

Abstract

The 2D lattice gauge theory with a quantum gauge group $SL_q(2)$ is considered. When $q=e^{i\frac{2\pi}{k+2}}$, its weak coupling partition function coincides with the one of the G/G coset model ({\em i.e.} equals the Verlinde numbers). However, despite such a remarkable coincidence, these models are not equivalent but, in some certain sense, dual to each other.