Adjoint quarks and fermionic boundary conditions

TL;DR

This study investigates the relationship between deconfinement and chiral symmetry restoration in SU(2) lattice gauge theory with adjoint fermions, revealing that deconfinement influences spectral properties and boundary condition dependence.

Contribution

It provides new insights into the spectral behavior of the Dirac operator and the role of boundary conditions across the deconfinement and chiral transition temperatures.

Findings

Chiral transition temperature is about four times the deconfinement temperature.

Spectral quantities depend on boundary conditions between the two transitions.

Deconfinement correlates with the onset of boundary condition dependence in spectral properties.

Abstract

We study quenched SU(2) lattice gauge theory with adjoint fermions in a wide range of temperatures. We focus on spectral quantities of the Dirac operator and use the temporal fermionic boundary conditions as a tool to probe the system. We determine the deconfinement temperature through the Polyakov loop, and the chiral symmetry restoration temperature for adjoint fermions through the gap in the Dirac spectrum. This chiral transition temperature is about four times larger than the deconfinement temperature. In between the two transitions we find that the system is characterized by a non-vanishing chiral condensate which differs for periodic and anti-periodic fermion boundary conditions. Only for the latter (physical) boundary conditions, the condensate vanishes at the chiral transition. The behavior between the two transitions suggests that deconfinement manifests itself as the onset of a dependence of spectral quantities of the Dirac operator on boundary conditions. This picture is supported further by our results for the dual chiral condensate.