Two dimensional fermions in four dimensional YM

TL;DR

This paper studies how two-dimensional Dirac fermions embedded in four-dimensional SU(N) Yang-Mills theory experience spontaneous chiral symmetry breaking as the size of the embedded torus varies, revealing insights into dimensional interactions.

Contribution

It introduces a novel setup of two-dimensional fermions in a four-dimensional gauge theory and analyzes the chiral symmetry breaking transition in the large N limit.

Findings

Chiral symmetry remains intact at small torus size.

Spontaneous chiral symmetry breaking occurs at large torus size.

The transition is studied in the large N limit.

Abstract

Dirac fermions in the fundamental representation of SU(N) live on a two dimensional torus flatly embedded in $R^4$. They interact with a four dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the size of the torus in units of $\frac{1}{\Lambda_{SU(N)}}$ is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit.