Intersections of thick Center Vortices, Dirac Eigenmodes and Fractional Topological Charge in SU(2) Lattice Gauge Theory

TL;DR

This paper investigates the relationship between thick SU(2) center vortex intersections, Dirac eigenmodes, and fractional topological charge, revealing that Dirac modes are sensitive to vortex structures but do not precisely locate fractional topological charges.

Contribution

It compares Dirac eigenmodes in different representations with vortex intersection configurations, highlighting their sensitivity and limitations in locating topological charge contributions.

Findings

Dirac eigenmodes are sensitive to vortex structures but do not precisely locate fractional topological charges.

Eigenmodes spread over the lattice, avoiding regions with negative Polyakov line traces.

Adjoint Dirac operator produces zero modes for |Q|=1/2 but does not localize them at single vortex intersections.

Abstract

Intersections of thick, plane SU(2) center vortices are characterized by the topological charge |Q|=1/2. We compare such intersections with the distribution of zeromodes of the Dirac operator in the fundamental and adjoint representation using both the overlap and asqtad staggered fermion formulations in SU(2) lattice gauge theory. We analyze configurations with four intersections and find that the probability density distribution of fundamental zeromodes in the intersection plane differs significantly from the one obtained analytically in [Phys.\ Rev.\ D 66, 85004 (2002)]. The Dirac eigenmodes are clearly sensitive to the traces of the Polyakov (Wilson) lines and do not exactly locate topological charge contributions. Although, the adjoint Dirac operator is able to produce zeromodes for configurations with topological charge |Q|=1/2, they do not locate single vortex intersections, as we prove by forming arbitrary linear combinations of these zeromodes - their scalar density peaks at least at two intersection points. With pairs of thin and thick vortices we realize a situation similar to configurations with topological charge |Q|=1/2. For such configurations the zeromodes do not localize in the regions of fractional topological charge contribution but spread over the whole lattice, avoiding regions of negative traces of Polyakov lines.