Two dimensional fermions in four dimensional YM

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.