Confinement and the quark Fermi-surface in SU(2N) QCD-like theories

TL;DR

This paper investigates the properties of SU(2N) QCD-like theories, showing that in the confinement phase, the quark determinant is boundary-condition independent for even N_c, and Fermi surfaces form only when center symmetry breaks.

Contribution

It demonstrates that in SU(2N) theories, the quark determinant's independence from boundary conditions in the confinement phase is a key property, and links Fermi surface formation to center symmetry breaking.

Findings

Quark determinant is boundary-condition independent for even N_c in confinement.

Fermi surfaces form only when center symmetry is broken.

Supported by lattice simulations for N_c=2 to 5.

Abstract

Yang-Mills theories with a gauge group SU(N_c\=3)and quark matter in the fundamental representation share many properties with the theory of strong interactions, QCD with N_c=3. We show that, for N_c even and in the confinement phase, the gluonic average of the quark determinant is independent of the boundary conditions, periodic or anti-periodic ones. We then argue that a Fermi sphere of quarks can only exist under extreme conditions when the centre symmetry is spontaneously broken and colour is liberated. Our findings are supported by lattice gauge simulations for N_c=2...5 and are illustrated by means of a simple quark model.