  It is well known that a weakly coupled U(N) gauge theory on a torus with
sides of length L has extra light states with energies of order 1/NL. We show
that a similar result holds for gauge theories on M/G where M is any compact
Riemannian manifold and G is any freely acting discrete isometry group. As in
the toroidal case, this is achieved by adding a suitable nontrivial flat
connection. As one application, we consider the AdS/CFT correspondence on
spacetimes asymptotic to AdS_5/G. By considering finite size effects at nonzero
temperature, we show that consistency requires these extra light states of the
gauge theory on S^3/G.
