Supermembrane limit of Yang-Mills theory

TL;DR

This paper demonstrates that in a specific limit, a Yang-Mills theory with super translation symmetry reduces to the action describing an M2-brane, linking gauge theory to membrane dynamics.

Contribution

It introduces a super-Yang-Mills framework on a product manifold that, under infrared scaling, reproduces M2-brane physics.

Findings

Yang-Mills theory reduces to M2-brane action in the infrared limit

Super translation group as the structure group in eleven dimensions

Connection between gauge theory and membrane dynamics

Abstract

We consider Yang-Mills theory with $N{=}1$ super translation group in eleven auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold $\Sigma_3\times S^1$, where $\Sigma_3$ is a three-dimensional Lorentzian manifold and $S^1$ is a circle. We show that in the infrared limit, when the metric on $S^1$ is scaled down, the Yang-Mills action supplemented by a Wess-Zumino-type term reduces to the action of an M2-brane.