# Anomaly constraints on deconfinement and chiral phase transition

## TL;DR

This paper uses 't Hooft anomalies to analyze constraints on thermal phase transitions in SU(N_c) gauge theories, revealing that certain symmetry restorations are impossible at specific temperatures and explaining dual magnetic gauge groups in some QCD cases.

## Contribution

It introduces a novel anomaly-based framework to constrain phase transitions in SU(N_c) gauge theories with different fermion representations and defines a new center-flavor symmetry.

## Key findings

- Chiral symmetry restoration cannot occur below deconfinement temperature for adjoint fermions.
- A modified center symmetry constrains phase transition behavior for fundamental fermions with gcd(N_c,N_f) ≠ 1.
- Partial explanation for dual magnetic gauge groups in supersymmetric QCD when gcd(N_c,N_f) ≠ 1.

## 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 ${\rm gcd}(N_c,N_f) \neq 1$.