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

TL;DR

This paper explores gauge theories on quotient manifolds and demonstrates that they possess extra light states similar to those on tori, with implications for the AdS/CFT correspondence and finite size effects at nonzero temperature.

Contribution

It generalizes the understanding of light states in gauge theories from tori to arbitrary compact Riemannian manifolds with discrete isometries, and discusses implications for AdS/CFT.

Findings

Gauge theories on M/G have extra light states with energies of order 1/NL.

Adding nontrivial flat connections reveals these light states.

Consistency of AdS/CFT on spacetimes asymptotic to AdS_5/G requires these states.

Abstract

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.