Colorful plane vortices and Chiral Symmetry Breaking in $SU(2)$ Lattice Gauge Theory

TL;DR

This paper studies colorful plane vortices in $SU(2)$ lattice gauge theory, demonstrating their topological properties and their role in spontaneous chiral symmetry breaking through analysis of low-lying Dirac modes.

Contribution

It introduces and analyzes colorful plane vortices, revealing their topological charge, gauge action, and impact on chiral symmetry breaking in lattice gauge theory.

Findings

Colorful plane vortices have topological charge $Q=-1$ in the continuum.

Lattice topological charge approaches $-1$ with increased vortex extent.

Low-lying Dirac modes indicate spontaneous chiral symmetry breaking.

Abstract

We investigate plane vortices with color structure. The topological charge and gauge action of such colorful plane vortices are studied in the continuum and on the lattice. These configurations are vacuum to vacuum transitions changing the winding number between the two vacua, leading to a topological charge $Q=-1$ in the continuum. After growing temporal extent of these vortices, the lattice topological charge approaches $-1$ and the index theorem is fulfilled. We analyze the low lying modes of the overlap Dirac operator in the background of these colorful plane vortices and compare them with those of spherical vortices. They show characteristic properties for spontaneous chiral symmetry breaking.