Note on Gauge Theories on M/G and the AdS/CFT Correspondence

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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 AdS₅/G. By considering finite size effects at nonzero temperature, we show that consistency requires these extra light states of the gauge theory on S³/G.