Abelian Dominance of Chiral Symmetry Breaking in Lattice QCD

TL;DR

This study investigates how Abelian monopoles influence chiral symmetry breaking in lattice QCD, showing that monopoles in maximal Abelian gauge can replicate the chiral condensate of the full non-Abelian theory.

Contribution

It demonstrates that Abelian monopoles in specific gauges can account for chiral symmetry breaking effects in lattice QCD, providing insight into Abelian dominance.

Findings

Monopoles in maximal Abelian gauge reproduce the chiral condensate of the non-Abelian theory.

Abelian projection in different gauges affects the representation of chiral symmetry breaking.

Results are consistent across SU(2) and SU(3) gauge groups.

Abstract

Calculations of the chiral condensate on the lattice using staggered fermions and the Lanczos algorithm are presented. Four gauge fields are considered: the quenched non-Abelian field, an Abelian projected field, and monopole and photon fields further decomposed from the Abelian field. Abelian projection is performed in maximal Abelian gauge and in Polyakov gauge. The results show that monopoles in maximal Abelian gauge largely reproduce the chiral condensate values of the full non-Abelian theory, in both SU(2) and SU(3) color.