# The topological susceptibility of two-dimensional $U(N)$ gauge theories

## TL;DR

This paper investigates the topological susceptibility in two-dimensional $U(N)$ gauge theories, providing explicit formulas and analyzing various limits including continuum, infinite volume, and large $N$.

## Contribution

It offers explicit expressions for the partition function and topological susceptibility at finite lattice spacing and volume, and explores their behavior in key limits.

## Key findings

- Explicit formulas for partition function and susceptibility
- Analysis of continuum and large N limits
- Results applicable to both abelian and non-abelian cases

## Abstract

In this paper we study the topological susceptibility of two-dimensional $U(N)$ gauge theories. We provide explicit expressions for the partition function and the topological susceptibility at finite lattice spacing and finite volume. We then examine the particularly simple case of the abelian $U(1)$ theory, the continuum limit, the infinite volume limit, and we finally discuss the large $N$ limit of our results.