Universality of Phases in QCD and QCD-like Theories

TL;DR

This paper demonstrates that the phase diagrams of QCD and QCD-like theories are universal in the large-N_c limit, allowing insights into QCD phase transitions through sign-free theories like finite isospin chemical potential.

Contribution

It establishes the universality of phase diagrams across different QCD-like theories via orbifold equivalence, enabling study of QCD phases using sign-free models.

Findings

Phase diagrams are identical between SU(N_c) QCD at finite isospin and SO(2N_c)/Sp(2N_c) theories at finite baryon chemical potential.

Universality holds in high-density regimes and in solvable random matrix models.

Sign-free theories can be used to study QCD critical points and phase transitions.

Abstract

We argue that the whole or the part of the phase diagrams of QCD and QCD-like theories should be universal in the large-N_c limit through the orbifold equivalence. The whole phase diagrams, including the chiral phase transitions and the BEC-BCS crossover regions, are identical between SU(N_c) QCD at finite isospin chemical potential and SO(2N_c) and Sp(2N_c) gauge theories at finite baryon chemical potential. Outside the BEC-BCS crossover region in these theories, the phase diagrams are also identical to that of SU(N_c) QCD at finite baryon chemical potential. We give examples of the universality in some solvable cases: (i) QCD and QCD-like theories at asymptotically high density where the controlled weak-coupling calculations are possible, (ii) chiral random matrix theories of different universality classes, which are solvable large-N (large volume) matrix models of QCD. Our results strongly suggest that the chiral phase transition and the QCD critical point at finite baryon chemical potential can be studied using sign-free theories, such as QCD at finite isospin chemical potential, in lattice simulations.