Chiral symmetry and spectral properties of the Dirac operator in G2 Yang-Mills Theory

TL;DR

This study investigates chiral symmetry breaking and spectral characteristics of the Dirac operator in G2 gauge theory, revealing temperature-dependent symmetry restoration and similarities with SU(N) behavior under specific boundary conditions.

Contribution

It provides the first detailed analysis of chiral symmetry and spectral properties in G2 Yang-Mills theory, highlighting the effects of boundary conditions and temperature.

Findings

Chiral symmetry is broken at low temperatures.

Chiral symmetry is restored above the phase transition.

Spectral quantities in G2 mirror those in SU(N) under certain conditions.

Abstract

We study spontaneous chiral symmetry breaking and the spectral properties of the staggered lattice Dirac operator using quenched gauge configurations for the exceptional group G2, which has a trivial center. In particular we study the system below and above the finite temperature transition and use the temporal boundary conditions of the fermions to probe the system. We evaluate several observables: The spectral density at the origin, the spectral gap, the chiral condensate and the recently proposed dual chiral condensate. We show that chiral symmetry is broken at low temperatures and is restored at high temperatures at the thermodynamic phase transition. Concerning the role of the boundary conditions we establish that in all respects the spectral quantities behave for G2 in exactly the same way as for SU(N), when for the latter group the gauge ensemble above T_c is restricted to the sector of configurations with real Polyakov loop.