Topological effects in continuum 2d $U(N)$ gauge theories

Abstract

We study the $\theta$ dependence of the continuum limit of 2d $U(N)$ gauge theories defined on compact manifolds, with special emphasis on spherical ($g=0$) and toroidal ($g=1$) topologies. We find that the coupling between $U(1)$ and $SU(N)$ degrees of freedom survives the continuum limit, leading to observable deviations of the continuum topological susceptibility from the $U(1)$ behavior, especially for $g=0$, in which case deviations remain even in the large $N$ limit.

7 pages, 6 eps figures

References in corpus (4)

• Topological Casimir effect in Maxwell Electrodynamics on a Compact Manifold
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• On the effective Lagrangian of CP^(N-1) models in the large N limit
• Correlation between Polyakov loops oriented in two different directions in SU(N) gauge theory on a two dimensional torus

Cited by in corpus (2)

• Tensor renormalization group and the volume independence in 2D U($N$) and SU($N$) gauge theories
• Topological sampling through windings