Two dimensional fermions in three dimensional YM

TL;DR

This paper investigates how two-dimensional Dirac fermions on a cylindrical surface interact with three-dimensional SU(N) Yang-Mills fields, revealing a spontaneous chiral symmetry breaking as the cylinder's circumference varies, with implications for higher-dimensional YM theories.

Contribution

It introduces a novel setup of surface fermions coupled to 3D YM and analyzes the chiral symmetry behavior, highlighting effects of dimensionality and large N limits.

Findings

Chiral symmetry is spontaneously broken at large N as the cylinder's circumference increases.

The setup preserves global chiral symmetry at finite N.

Replacing 3D YM with 4D YM affects renormalization properties.

Abstract

Dirac fermions in the fundamental representation of SU(N) live on the surface of a cylinder embedded in $R^3$ and interact with a three dimensional SU(N) Yang Mills vector potential preserving a global chiral symmetry at finite $N$. As the circumference of the cylinder is varied from small to large, the chiral symmetry gets spontaneously broken in the infinite $N$ limit at a typical bulk scale. Replacing three dimensional YM by four dimensional YM introduces non-trivial renormalization effects.