Local correlation among the chiral condensate, monopoles, and color magnetic fields in Abelian projected QCD

TL;DR

This study explores the local relationship between the chiral condensate, monopoles, and magnetic fields in lattice QCD, revealing strong correlations and suggesting magnetic fields enhance chiral symmetry breaking.

Contribution

It demonstrates a strong positive correlation between the chiral condensate and magnetic fields in Abelian projected QCD, supported by lattice simulations and idealized models.

Findings

Chiral condensate localizes near magnetic fields and monopoles.

Strong correlation coefficient (~0.8) between chiral condensate and magnetic quantity.

Chiral condensate is enhanced by magnetic fields around monopoles, akin to magnetic catalysis.

Abstract

Using the lattice gauge field theory, we study the relation among the local chiral condensate, monopoles, and color magnetic fields in quantum chromodynamics (QCD). First, we investigate idealized Abelian gauge systems of 1) a static monopole-antimonopole pair and 2) a magnetic flux without monopoles, on a four-dimensional Euclidean lattice. In these systems, we calculate the local chiral condensate on quasi-massless fermions coupled to the Abelian gauge field, and find that the chiral condensate is localized in the vicinity of the magnetic field. Second, using SU(3) lattice QCD Monte Carlo calculations, we investigate Abelian projected QCD in the maximally Abelian gauge, and find clear correlation of distribution similarity among the local chiral condensate, monopoles, and color magnetic fields in the Abelianized gauge configuration. As a statistical indicator, we measure the correlation coefficient $r$, and find a strong positive correlation of $r \simeq 0.8$ between the local chiral condensate and an Euclidean color-magnetic quantity ${\cal F}$ in Abelian projected QCD. The correlation is also investigated for the deconfined phase in thermal QCD. As an interesting conjecture, like magnetic catalysis, the chiral condensate is locally enhanced by the strong color-magnetic field around the monopoles in QCD.