Anomaly constraints on deconfinement and chiral phase transition

We study constraints on thermal phase transitions of $\mathrm{S}\mathrm{U}(N_c)$ 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 $\mathrm{g}\mathrm{c}\mathrm{d}(N_c,N_f)\mathrm{\ne }1$. 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 group in (supersymmetric) QCD when $\mathrm{g}\mathrm{c}\mathrm{d}(N_c,N_f)\mathrm{\ne }1$.