Dependence of Dirac eigenmodes on boundary conditions for SU(2) lattice gauge theory

TL;DR

This study investigates how boundary conditions affect the localization and position of Dirac zero modes in SU(2) lattice gauge theory, revealing that boundary choices significantly influence zero mode localization and can cause positional jumps.

Contribution

It demonstrates the dependence of Dirac zero mode localization and position on boundary conditions in SU(2) lattice gauge theory, highlighting boundary effects on topological features.

Findings

Zero modes are highly localized in all four directions.

Boundary conditions significantly influence zero mode positions.

Positions of zero modes jump in about one third of configurations when boundary conditions change.

Abstract

We analyze zero modes of the Dirac operator for SU(2) lattice gauge theory. We find that the zero modes are strongly localized in all 4 directions. The position of these lumps depends on the boundary conditions we use for the Dirac operator. We compare periodic boundary conditions and anti-periodic boundary conditions and find that the position of the zero modes jumps for about one third of the configurations.