Center vortex model for the infrared sector of Yang-Mills theory - Quenched Dirac spectrum and chiral condensate

TL;DR

This paper develops a Dirac operator within the center vortex model for SU(2) Yang-Mills theory, successfully reproducing key confinement and chiral symmetry breaking features, including temperature-dependent chiral condensate behavior.

Contribution

It introduces a Dirac operator for vortex surfaces and demonstrates its effectiveness in modeling the quenched Dirac spectrum and chiral condensate in SU(2) gauge theory.

Findings

Reproduces confinement and topological susceptibility

Models temperature dependence of chiral condensate

Aligns with lattice Yang-Mills measurements

Abstract

The Dirac operator describing the coupling of continuum quark fields to SU(2) center vortex world-surfaces composed of elementary squares on a hypercubic lattice is constructed. It is used to evaluate the quenched Dirac spectral density in the random vortex world-surface model, which previously has been shown to quantitatively reproduce both the confinement properties and the topological susceptibility of SU(2) Yang-Mills theory. Under certain conditions on the modeling of the vortex gauge field, a behavior of the quenched chiral condensate as a function of temperature is obtained which is consistent with measurements in SU(2) lattice Yang-Mills theory.