Topological lumps and Dirac zero modes in SU(3) lattice gauge theory on the torus

TL;DR

This study investigates how boundary conditions affect Dirac zero modes in SU(3) lattice gauge theory on a 4-torus, revealing that zero modes can interact with multiple topological objects, possibly fractional charges.

Contribution

It demonstrates the boundary condition dependence of zero modes and suggests that a single topological charge 1 configuration can couple to multiple lumps, indicating complex topological structures.

Findings

Zero modes strongly depend on boundary conditions.

Lumps change position with boundary condition variations.

Zero modes can couple to multiple objects, possibly fractional charges.

Abstract

We compute eigenmodes of the lattice Dirac operator for quenched SU(3) gauge configurations on the 4-torus with topological charge 1. We find a strong dependence of the zero modes on the boundary conditions which we impose for the Dirac operator. The lumps seen by the eigenmodes often change their position when changing the boundary conditions, while the local chirality of the lumps remains the same. Our results show that the zero mode of a charge 1 configuration can couple to more than one object. We address the question whether these objects could be fractionally charged lumps.