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

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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.