Anomaly constraints on deconfinement and chiral phase transition

Abstract

We study the constraints on thermal phase transitions of $\mathrm{SU}({N}_{c})$ gauge theories by using the 't Hooft anomaly involving the center symmetry and chiral symmetry. We consider two cases of massless fermions: (i) adjoint fermions and (ii) ${N}_{f}$ flavors of fundamental fermions with a nontrivial greatest common divisor, $\mathrm{gcd}({N}_{c},{N}_{f})\ensuremath{\ne}1$. For the first case (i), we show that the chiral symmetry restoration in terms of the standard Landau-Ginzburg effective action is impossible at a temperature lower than that of deconfinement. For the second case (ii), we introduce a modified version of the center symmetry, which we call center-flavor symmetry, and draw similar conclusions under a certain definition of confinement. Moreover, at zero temperature, our results give a partial explanation of the appearance of dual magnetic gauge groups in (supersymmetric) QCD when $\mathrm{gcd}({N}_{c},{N}_{f})\ensuremath{\ne}1$.