Anomaly constraints on deconfinement and chiral phase transition

TL;DR

The work leverages a mixed 't Hooft anomaly between center and chiral symmetries to place rigorous constraints on thermal phase transitions in SU($N_c$) gauge theories. By analyzing adjoint fermions and, separately, fundamental fermions with gcd($N_c$, $N_f$) ≠ 1 via a center-flavor construction, it shows that chiral restoration cannot occur below deconfinement under conventional LG descriptions and derives an inequality $T_{deconf} \le T_{chiral}$. The results provide a unified anomaly-based mechanism for constraining phase structure, illuminate the role of fractional instantons and background fields, and offer a partial explanation for the emergence of dual magnetic gauge groups in (supersymmetric) QCD when gcd($N_c$, $N_f$) ≠ 1. These insights have potential implications for understanding confinement, chiral dynamics, and dual descriptions across both supersymmetric and non-supersymmetric gauge theories.

Abstract

We study constraints on thermal phase transitions of ${\rm SU}(N_c)$ 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 ${\rm gcd}(N_c,N_f) \neq 1$. 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 ${\rm gcd}(N_c,N_f) \neq 1$.