Evidence that centre vortices underpin dynamical chiral symmetry breaking in $\mathrm{SU}(3)$ gauge theory

TL;DR

This study demonstrates that centre vortices are essential for dynamical chiral symmetry breaking in SU(3) gauge theory, using overlap fermions to reveal the interplay between vortices, instantons, and mass generation.

Contribution

It provides new evidence linking centre vortices to chiral symmetry breaking by employing overlap fermions and vortex removal, highlighting the importance of vortex-instanton interactions.

Findings

Vortex removal leads to loss of chiral symmetry breaking with overlap fermions.

Vortex-only backgrounds can generate instantons after smoothing.

Visualizations show a link between vortex and instanton structures.

Abstract

The link between dynamical chiral symmetry breaking and centre vortices in the gauge fields of pure $\mathrm{SU}(3)$ gauge theory is studied using the overlap-fermion quark propagator in Lattice QCD. Overlap fermions provide a lattice realisation of chiral symmetry and consequently offer a unique opportunity to explore the interplay of centre vortices, instantons and dynamical mass generation. Simulations are performed on gauge fields featuring the removal of centre vortices, identified through gauge transformations maximising the center of the gauge group. In contrast to previous results using the staggered-fermion action, the overlap-fermion results illustrate a loss of dynamical chiral symmetry breaking coincident with vortex removal. This result is linked to the overlap-fermion's sensitivity to the subtle manner in which instanton degrees of freedom are compromised through the process of centre vortex removal. Backgrounds consisting solely of the identified centre vortices are also investigated. After smoothing the vortex-only gauge fields, we observe dynamical mass generation on the vortex-only backgrounds consistent within errors with the original gauge-field ensemble following the same smoothing. Through visualizations of the instanton-like degrees of freedom in the various gauge-field ensembles, we find evidence of a link between the centre vortex and instanton structure of the vacuum. While vortex removal destabilizes instanton-like objects under ${\cal O}(a^4)$-improved cooling, vortex-only backgrounds provide gauge-field degrees of freedom sufficient to create instantons upon cooling.