Patterns of Spontaneous Chiral Symmetry Breaking in Vectorlike Gauge Theories

TL;DR

This study tests a conjecture that chiral symmetry breaking in vectorlike gauge theories falls into three classes, using lattice simulations of SU(2), SU(3), and SU(4) gauge groups with staggered fermions.

Contribution

It provides numerical evidence supporting the conjectured classification of spontaneous chiral symmetry breaking patterns across different gauge groups and fermion representations.

Findings

Confirmed the three classes of symmetry breaking patterns.

Identified correct and incorrect symmetry breaking classes for staggered fermions.

Validated the use of Dirac eigenvalue distributions as signals for symmetry breaking.

Abstract

It has been conjectured that spontaneous chiral symmetry breaking in strongly coupled vectorlike gauge theories falls into only three different classes, depending on the gauge group and the representations carried by the fermions. We test this proposal by studying SU(2), SU(3) and SU(4) lattice gauge theories with staggered fermions in different irreducible representations. Staggered fermions away from the continuum limit should, for all complex representations, still belong to the continuum class of spontaneous symmetry breaking. But for all real and pseudo-real representations we show that staggered fermions should belong to incorrect symmetry breaking classes away from the continuum, thus generalizing previous results. As an unambiguous signal for whether chiral symmetry breaks, and which breaking pattern it follows, we look at the smallest Dirac eigenvalue distributions. We find that the patterns of symmetry breaking are precisely those conjectured.