Numerical study of chiral symmetry breaking in non-Abelian gauge theory with background magnetic field

TL;DR

This study explores how a uniform magnetic field influences chiral symmetry breaking in SU(2) Yang-Mills theory, revealing a linear increase in the chiral condensate with field strength and changes in eigenmode structure.

Contribution

It provides the first lattice investigation of magnetic field effects on chiral symmetry breaking in SU(2) gauge theory, confirming theoretical predictions and analyzing eigenmode behavior.

Findings

Chiral condensate grows linearly with magnetic field strength up to 3 GeV.

The coefficient of the linear growth decreases with increasing temperature.

Near-zero eigenmodes become more regular and delocalized in magnetic fields.

Abstract

We investigate the effect of a uniform background magnetic field on the chiral symmetry breaking in SU(2) Yang-Mills theory on the lattice. We observe that the chiral condensate grows linearly with the field strength B up to \sqrt{e B} = 3 GeV as predicted by chiral perturbation theory for full QCD. As the temperature increases the coefficient in front of the linear term gets smaller. In the magnetic field near-zero eigenmodes of the Dirac operator tend to have more regular structure with larger (compared to zero-field case) Hausdorff dimensionality. We suggest that the delocalization of near-zero eigenmodes plays a crucial role in the enhancement of the chiral symmetry breaking.