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

TL;DR

This paper investigates how topological effects influence the continuum limit of 2D $U(N)$ gauge theories on different manifolds, revealing persistent deviations in topological susceptibility due to coupling between $U(1)$ and $SU(N)$ components.

Contribution

It demonstrates that the coupling between $U(1)$ and $SU(N)$ degrees of freedom persists in the continuum limit, affecting topological susceptibility especially on spherical topology.

Findings

Coupling between $U(1)$ and $SU(N)$ persists in continuum limit.

Deviations in topological susceptibility are significant for spherical topology.

Deviations remain even at large $N$ for $g=0$.

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.