A Large N Chiral Transition on a Plaquette

TL;DR

This paper models a chiral transition using a large N limit in a 2D lattice gauge theory, revealing symmetry breaking at strong coupling and restoration at weak coupling as N approaches infinity.

Contribution

It introduces a simplified single-plaquette model with Grassmann variables and phase factors to study chiral symmetry behavior in the large N limit.

Findings

Chiral symmetry is broken at strong coupling.

Chiral symmetry is restored at weak coupling as N approaches infinity.

The model captures the phase transition behavior of chiral symmetry.

Abstract

We construct a model of a chiral transition using the well known large N transition in two dimensional U(N) lattice gauge theory. Restricting the model to a single plaquette, we introduce Grassmann variables on the corners of the plaquette with the natural phase factors of staggered fermions and couple them to the U(N) link variables. The classical theory has a continuous chiral symmetry which is broken at strong couplings, but is restored for weak couplings in the $N \to \infty$ limit.