D2 to D2

TL;DR

This paper derives a ghost-free Lorentzian 3-algebra theory from maximally supersymmetric (2+1)d Yang-Mills theory using a duality transformation, providing a new perspective on M2-brane descriptions.

Contribution

It presents a derivation of the Lorentzian 3-algebra theory directly from SYM without relying on 3-algebra properties, clarifying its relation to M2-branes.

Findings

The theory is equivalent to SYM on-shell.

It exhibits enhanced R-symmetry and superconformal symmetry off-shell.

The derivation does not depend on properties of 3-algebras.

Abstract

Starting from maximally supersymmetric (2+1)d Yang-Mills theory and using a duality transformation due to de Wit, Nicolai and Samtleben, we obtain the ghost-free Lorentzian 3-algebra theory that has recently been proposed to describe M2-branes. Our derivation does not invoke any properties of 3-algebras. Being derivable from SYM, the final theory is manifestly equivalent to it on-shell and should not be thought of as the IR limit that describes M2-branes, though it does have enhanced R-symmetry as well as superconformal symmetry off-shell.