M2 to D2

TL;DR

This paper demonstrates how a scalar field in a 3-algebra field theory for M2-branes, when acquiring a vacuum expectation value, induces a Higgs mechanism that transforms topological Chern-Simons gauge fields into dynamical Yang-Mills fields, connecting M2 and D2-brane theories.

Contribution

It provides a detailed derivation of maximally supersymmetric Yang-Mills theory from the 3-algebra M2-brane framework via a novel Higgs mechanism.

Findings

Higgs mechanism promotes Chern-Simons to Yang-Mills fields.

Derivation of D2-brane Yang-Mills theory from M2-brane 3-algebra theory.

Establishes a link between 3-algebras and Yang-Mills theories.

Abstract

We examine the recently proposed "3-algebra" field theory for multiple M2-branes and show that when a scalar field valued in the 3-algebra develops a vacuum expectation value, the resulting Higgs mechanism has the novel effect of promoting topological (Chern-Simons) to dynamical (Yang-Mills) gauge fields. This leads to a precise derivation of the maximally supersymmetric Yang-Mills theory on multiple D2-branes and thereby provides a relationship between 3-algebras and Yang-Mills theories. We discuss the physical interpretation of this result.