Embedded monopoles in quark eigenmodes in SU(2) Yang-Mills Theory

TL;DR

This paper investigates embedded QCD monopoles in SU(2) Yang-Mills theory using lattice simulations, revealing their density behavior across phases and their relation to chiral symmetry restoration.

Contribution

It provides a detailed numerical analysis of embedded monopoles, their scaling, and their gluonic structure in different temperature phases of SU(2) Yang-Mills theory.

Findings

Monopole densities are anti-correlated with Dirac eigenmode density.

Embedded monopoles are dense in the chirally invariant phase and dilute in the broken phase.

Monopoles scale differently: scalar and axial as strings, chirally invariant as membranes.

Abstract

We study the embedded QCD monopoles (``quark monopoles'') using low-lying eigenmodes of the overlap Dirac operator in zero- and finite-temperature SU(2) Yang-Mills theory on the lattice. These monopoles correspond to the gauge-invariant hedgehogs in the quark-antiquark condensates. The monopoles were suggested to be agents of the chiral symmetry restoration since their cores should suppress the chiral condensate. We study numerically the scalar, axial and chirally invariant definitions of the embedded monopoles and show that the monopole densities are in fact globally anti-correlated with the density of the Dirac eigenmodes. We observe, that the embedded monopoles corresponding to low-lying Dirac eigenvalues are dense in the chirally invariant (high temperature) phase and dilute in the chirally broken (low temperature) phase. We find that the scaling of the scalar and axial monopole densities towards the continuum limit is similar to the scaling of the string-like objects while the chirally invariant monopoles scale as membranes. The excess of gluon energy at monopole positions reveals that the embedded QCD monopole possesses a gluonic core, which is, however, empty at the very center of the monopole.