Two dimensional lattice gauge theory based on a quantum group

TL;DR

This paper develops a two-dimensional lattice gauge theory using quantum groups, defining gauge algebra, Wilson loops, and computing the partition function on Riemann surfaces, revealing connections to Chern-Simons theory.

Contribution

It introduces a novel lattice gauge theory framework based on quantum groups, with explicit calculations of Wilson loops and partition functions on Riemann surfaces.

Findings

Partition function computed explicitly for various surfaces

Wilson loops defined within the quantum group framework

The theory shows a relation to Chern-Simons theory

Abstract

In this article we analyze a two dimensional lattice gauge theory based on a quantum group.The algebra generated by gauge fields is the lattice algebra introduced recently by A.Yu.Alekseev,H.Grosse and V.Schomerus we define and study wilson loops and compute explicitely the partition function on any Riemann surface. This theory appears to be related to Chern-Simons Theory.