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

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.