QCD Topology at Finite Temperature: Statistical Mechanics of Selfdual Dyons

TL;DR

This paper develops a statistical mechanics model of self-dual dyons in finite-temperature QCD, performing Monte Carlo simulations to explore their correlations and impact on the Dirac spectrum, shedding light on topological phenomena.

Contribution

It introduces the first numerical Monte Carlo simulations of a dyon ensemble including Coulomb interactions, screening, and fermion modes, advancing understanding of topological effects in gauge theories.

Findings

Dyon correlations depend on density and quark flavors.

Dirac spectrum varies with dyon ensemble diluteness.

Model supports the role of dyons in chiral symmetry breaking.

Abstract

Topological phenomena in gauge theories have long been recognized as the driving force for chiral symmetry breaking and confinement. These phenomena can be conveniently investigated in the semi-classical picture, in which the topological charge is entirely carried by (anti-)self-dual gauge configurations. In such an approach, it has been shown that near the critical temperature, the non-zero expectation value of the Polyakov loop (holonomy) triggers the "Higgsing" of the color group, generating the splitting of instantons into $N_c$ self-dual dyons. A number of lattice simulations have provided some evidence for such dyons, and traced their relation with specific observables, such as the Dirac eigenvalue spectrum. In this work, we formulate a model, based on one-loop partition function and including Coulomb interaction, screening and fermion zee modes. We then perform the first numerical Monte Carlo simulations of a statistical ensemble of self-dual dyons,as a function of their density, quark mass and the number of flavors. We study different dyonic two-point correlation functions and we compute the Dirac spectrum, as a function of the ensemble diluteness and the number of quark flavors.