Critical analysis of topological charge determination in the background of center vortices in SU(2) lattice gauge theory

Abstract

We analyze topological charge contributions from classical SU(2) center vortices with shapes of planes and spheres using different topological charge definitions, namely the center vortex picture of topological charge, a discrete version of FF in the plaquette and hypercube definitions and the lattice index theorem. For the latter the zeromodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations are investigated. We find several problems for the individual definitions and discuss the discrepancies between the different topological charge definitions. Our results show that the interpretation of topological charge in the background of center vortices is rather subtle.

8 pages, 8 figures

References in corpus (3)

• Intersections of thick Center Vortices, Dirac Eigenmodes and Fractional Topological Charge in SU(2) Lattice Gauge Theory
• Tests of the lattice index theorem
• Fractal dimension of the topological charge density distribution in SU(2) lattice gluodynamics

Cited by in corpus (12)

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• A model of random center vortex lines in continuous 2+1-dimensional space-time
• Confining Bond Rearrangement in the Random Center Vortex Model
• Smearing Center Vortices
• Approaching $SU(2)$ gauge dynamics with smeared $Z(2)$ vortices
• Combining the color structures and intersection points of thick center vortices and low-lying Dirac modes
• A first analysis of the ensemble of local maxima of maximal center gauge
• Comment on "Fractional topological charges and the lowest Dirac modes"
• Fractional topological charges and the lowest Dirac modes