Center vortex influence on the Dirac spectrum

TL;DR

This paper investigates how center vortices affect the low-lying eigenmodes of the Dirac operator in lattice QCD, revealing formulation-dependent effects and correlations with vortex locations.

Contribution

It provides a comparative analysis of the impact of center vortices on Dirac eigenmodes across different fermion formulations and extends previous findings on vortex-eigenmode correlations.

Findings

Low-lying near-zero modes are present in staggered formulation but not in overlap on projected configurations.

Strong correlations exist between vortex locations and low-lying eigenmode densities.

Eigenmodes tend to concentrate in point-like regions rather than higher-dimensional submanifolds.

Abstract

We study the influence of center vortices on the low-lying eigenmodes of the Dirac operator, in both the overlap and asqtad formulations. For center-projected configurations, one finds that the low-lying near-zero modes are present in the staggered (asqtad) formulation, but not in the overlap and "chirally-improved" formulations. We argue that this is due to the absence of a field-independent chiral symmetry in the latter formulations, when the Dirac operator is evaluated on the very rough configurations generated by center projection. We also confirm and extend the results of Kovalenko et al. [Phys. Lett. B 648, 383 (2007)], finding strong correlations between center vortex locations, and the scalar density of low-lying Dirac eigenmodes on unprojected lattices, in both asqtad and overlap formulations. It is found that the low-lying eigenmodes have their largest concentrations in point-like regions, rather than on submanifolds of higher dimensionality.