Topological effects in continuum two-dimensional U(N) gauge theories

We study the θ dependence of the continuum limit of 2D UðNÞ gauge theories defined on compact manifolds, with special emphasis on spherical (g ¼ 0) and toroidal (g ¼ 1) topologies. We find that the coupling between Uð1Þ and SUðNÞ degrees of freedom survives the continuum limit, leading to observable deviations of the continuum topological susceptibility from the Uð1Þ behavior, especially for g ¼ 0, in which case deviations remain even in the large N limit.