Center vortices and Dirac eigenmodes in SU(2) lattice gauge theory
Jochen Gattnar, Christof Gattringer, Kurt Langfeld, Hugo Reinhardt,, Andreas Schafer, Stefan Solbrig, and T. Tok
TL;DR
This paper investigates how center vortices influence Dirac eigenmodes in SU(2) lattice gauge theory, revealing that vortex removal destroys topological modes and alters the Dirac spectrum, impacting chiral symmetry breaking.
Contribution
It demonstrates the crucial role of center vortices in generating topological zero modes and shaping the Dirac spectrum in SU(2) lattice gauge theory.
Findings
Vortex removal destroys zero modes and topological near zero modes.
Vortex-removed configurations resemble free spectra with vanishing chiral condensate.
Smooth vortex configurations produce zero and near zero modes.
Abstract
We study the interplay between Dirac eigenmodes and center vortices in SU(2) lattice gauge theory. In particular we focus on vortex-removed configurations and compare them to an ensemble of configurations with random changes of the link variables. We show that removing the vortices destroys all zero modes and the near zero modes are no longer coupled to topological structures. The Dirac spectrum for vortex-removed configurations in many respects resembles a free spectrum thus leading to a vanishing chiral condensate. Configurations with random changes leave the topological features of the Dirac eigensystem intact. We finally show that smooth center vortex configurations give rise to zero modes and topological near zero modes.
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