Anomaly constraints on deconfinement and chiral phase transition

We study the constraints on thermal phase transitions of SU (N₂) 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) N₅ flavors of fundamental fermions with a nontrivial greatest common divisor, gcd (N₂, N₅) 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 gcd (N₂, N₅) 1.