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.

arXiv comment11 pages, 7 eps figures

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• Topological sampling through windings
• The Large $N_c$ limit of QCD on the lattice
• Gauge invariant input to neural network for path optimization method
• Density of states approach for lattice gauge theory with a $\theta$-term
• Improving efficiency of the path optimization method for a gauge theory
• Topological effects in continuum 2d $U(N)$ gauge theories
• Compact Gauge Fields on Causal Dynamical Triangulations: a 2D case study
• Complex Langevin analysis of 2D U(1) gauge theory on a torus with a $\theta$ term