Chiral symmetry breaking at large N_c

TL;DR

This paper provides numerical evidence that in the large N_c limit, four-dimensional Yang-Mills theory on a finite four-torus exhibits spontaneous chiral symmetry breaking when the torus size exceeds a critical length, with a condensate independent of volume.

Contribution

It demonstrates that chiral symmetry breaking occurs at finite volume in the large N_c limit, supporting volume reduction for the chiral condensate in Yang-Mills theory.

Findings

Chiral symmetry breaks spontaneously above a critical torus size l_c.

Chiral condensate value is independent of the torus size l.

Spontaneous symmetry breaking occurs at finite volume in the large N_c limit.

Abstract

We present numerical evidence for the hypothesis that, in the planar limit, four dimensional Euclidean Yang-Mills theory on a finite symmetrical four-torus breaks chiral symmetry spontaneously when the length of the sides l is larger than a critical value l_c with a bilinear condensate whose value is independent of l. Therefore spontaneous symmetry breaking occurs at finite volume and infinite N_c reduction holds for the chiral condensate.