Topology and chiral symmetry breaking in SU(N) gauge theories

TL;DR

This study investigates how topological charge and chiral symmetry breaking behave in SU(N) gauge theories with N=2 to 5, revealing that local chirality diminishes as N increases and instanton resolution is limited by a critical size.

Contribution

It introduces a fermionic definition of topological charge using the overlap Dirac operator and analyzes its agreement with cooling methods across different N, highlighting the N-dependence of instanton resolution and chirality.

Findings

Disagreement between fermionic and cooling topological charges decreases with N.

The Dirac operator resolves instantons larger than about 2.5a in size.

Local chirality of near-zero modes weakens and vanishes as N approaches infinity.

Abstract

We study the low-lying eigenmodes of the lattice overlap Dirac operator for SU(N) gauge theories with N=2,3,4 and 5 colours. We define a fermionic topological charge from the zero-modes of this operator and show that, as N grows, any disagreement with the topological charge obtained by cooling the fields, becomes rapidly less likely. By examining the fields where there is a disagreement, we are able to show that the Dirac operator does not resolve instantons below a critical size of about rho = 2.5 a, but resolves the larger, more physical instantons. We investigate the local chirality of the near-zero modes and how it changes as we go to larger N. We observe that the local chirality of these modes, which is prominent for SU(2) and SU(3), becomes rapidly weaker for larger N and is consistent with disappearing entirely in the limit of N -> infinity. We find that this is not due to the observed disappearance of small instantons at larger N.