The chiral condensate from the Dirac spectrum in BSM gauge theories

TL;DR

This study investigates chiral symmetry breaking in a BSM SU(3) gauge theory with sextet fermions by analyzing Dirac eigenvalues, revealing evidence of spontaneous symmetry breaking but also highlighting discrepancies in condensate measurements.

Contribution

It applies Dirac spectrum analysis to a BSM gauge theory with sextet fermions, providing new insights into chiral symmetry breaking and identifying measurement discrepancies.

Findings

Eigenvalue density indicates spontaneous symmetry breaking.

Discrepancy between eigenvalue spectrum and direct condensate measurements.

Initial results at a single lattice spacing.

Abstract

The eigenvalues of the Dirac operator at finite volume encode whether or not chiral symmetry is spontaneously broken in a massless theory. We apply this framework in a particular BSM context, namely SU(3) gauge theory with N_f=2 massless flavors in the 2-index symmetric (sextet) representation. Our first results are at a single lattice spacing. We find that both the density of near-zero eigenvalues and the renormalization group invariant mode number indicate spontaneous symmetry breaking. Quantitatively, there is a discrepancy between the determination of the fermion condensate in the chiral limit via the eigenvalue spectrum and the determinations from direct measurements of the chiral condensate and the GMOR relation. We comment on possible explanations of this discrepancy and further refinements of this study.