Colorful SU(2) center vortices in the continuum and on the lattice

TL;DR

This paper generalizes the spherical vortex to a continuum form, investigates its properties, and discusses implications for lattice gauge theory and Monte Carlo configurations, addressing discrepancies in topological charge calculations.

Contribution

It introduces a continuum formulation of the spherical vortex and clarifies discretization effects causing topological charge discrepancies in lattice simulations.

Findings

Discrepancy between lattice topological charge and Dirac index is a discretization effect.

Continuum form of the spherical vortex is derived and analyzed.

Implications for Monte Carlo configurations are discussed.

Abstract

The spherical vortex as introduced in [Phys. Rev. D77, 014515 (2008)] is generalized. A continuum form of the spherical vortex is derived and investigated in detail. The discrepancy between the gluonic lattice topological charge and the index of the lattice Dirac operator described in previous papers is identified as a discretization effect. The importance of the investigations for Monte Carlo configurations is discussed.