Abelian Dominance in Chiral Symmetry Breaking

TL;DR

This paper investigates how Abelian monopoles influence chiral symmetry breaking by comparing lattice calculations of the chiral condensate across different gauge field configurations, revealing monopoles' significant role.

Contribution

It demonstrates that Abelian monopoles can largely reproduce the chiral condensate of the full non-Abelian theory, highlighting their importance in chiral symmetry breaking.

Findings

Abelian monopoles reproduce the chiral condensate values of the non-Abelian theory.

The study uses lattice calculations with staggered fermions and the Lanczos algorithm.

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

Abstract

Calculations of the chiral condensate $\langle \bar{\psi} \psi \rangle$ on the lattice using staggered fermions and the Lanczos algorithm are presented. Three gauge fields are considered: the quenched non-Abelian field, the Abelian field projected in the maximal Abelian gauge, and the monopole field further decomposed from the Abelian field. The results show that the Abelian monopoles largely reproduce the chiral condensate values of the full non-Abelian theory, both in SU(2) and in SU(3).