Chiral symmetry breaking and topology for all N

TL;DR

This paper explores how topology influences chiral symmetry breaking in SU(N) gauge theories at large N, using lattice simulations with overlap fermions to analyze zero modes and low-lying Dirac operator modes.

Contribution

It demonstrates that topology drives chiral symmetry breaking at N=3 and large N, and confirms the robustness of these results across different volumes and lattice spacings.

Findings

Topology drives chiral symmetry breaking at N=3 and large N

Results are consistent across volumes and lattice spacings

Addresses the role of instantons in topology description

Abstract

We investigate spontaneous chiral symmetry breaking in SU(N) gauge theories at large N using overlap fermions. The exact zero modes and the low-lying modes of the Dirac operator provide the tools to gain insight into the interplay between chiral symmetry breaking and topology. We find that topology indeed drives chiral symmetry breaking at N=3 as well as at large N. By comparing the results on various volumes and at different lattice spacings we are able to show that our conclusions are not affected by finite volume effects and also hold in the continuum limit. We then address the question whether the topology can be usefully described in terms of instantons.