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

TL;DR

This paper investigates the relationship between topological objects like instantons and the low-lying Dirac operator modes in SU(N) gauge theories, revealing that instanton content diminishes with increasing N.

Contribution

It provides a detailed analysis of instanton size distributions and their impact on Dirac modes across different SU(N) gauge theories, highlighting the N-dependent behavior.

Findings

Near-zero Dirac modes depend on topology for all N

Instanton size distribution varies with N

Small instanton content decreases as N increases

Abstract

We address the question of whether the low modes of the Dirac operator are caused by topological objects such as instantons in SU(N) gauge theories. We study the pseudo-scalar density of these modes, finding the size distributions of the instantons, and comparing it with the underlying gauge field. We find that, although the near-zero modes of the Dirac operator depend on topology for all N, their small instanton content decreases as N increases.