Chiral Symmetry Breaking in Abelian-Projected SU(2) Lattice Gauge Theory

TL;DR

This paper investigates chiral symmetry breaking in SU(2) lattice gauge theory, showing that Abelian projection in maximal Abelian gauge reproduces key nonabelian features, while field strength gauge projections do not scale properly.

Contribution

It demonstrates that maximal Abelian gauge projection captures chiral symmetry breaking parameters similar to the full nonabelian theory, unlike field strength gauge projection.

Findings

Maximal Abelian gauge projected fields yield chiral condensates similar to nonabelian theory.

Field strength gauge projections produce condensates insensitive to $eta$ and quark mass.

Maximal Abelian gauge reproduces meson correlators for small quark masses.

Abstract

Chiral symmetry breaking parameters are calculated in quenched SU(2) gauge theory and with Abelian gauge fields projected in maximal Abelian gauge and in field strength gauge. Maximal Abelian gauge projected fields lead to chiral condensate values which are quite similar to those of the full nonabelian theory. Pseudoscalar and vector meson correlators are calculated and found to be reproduced by the use of maximal Abelian gauge fields for small quark masses. In field-strength gauge, Abelian-projected fields give a chiral condensate which closely resembles the results of strongly coupled ($\beta<1$) gauge theory: the chiral condensate is insensitive to $\beta$ and quark mass and hence violates scaling badly.