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On comparing the phase diagram of SU(N) gauge theories at weak and strong coupling


Obtaining the phase diagram of QCD and QCD-like theories is complicated by the fact that the coupling-strength is large at low energies such that large volume perturbation theory is not valid in this limit. However, if an SU(N) gauge theory is compactified on a manifold with small spatial volume such as a sphere then the theory becomes weakly coupled, and the weak-coupling analogue of the confinement-deconfinement transition becomes accessible in the large N limit. We perform a one-loop perturbative calculation of SU(N) gauge theory with adjoint representation fermions (adjoint QCD) on S^1 x S^3 at large, and small N, and compare with recent lattice results. Adjoint QCD with periodic boundary conditions applied to massive fermions is particularly useful for this task as the phase diagram is quite rich including not only the confined and deconfined phases, but partially confined phases as well. We also discuss the implications for large N volume reduction in adjoint QCD. The technique presented is quite general and can also be applied to QCD and other QCD-like theories.