D2 to D2

TL;DR

This work shows that the ghost-free Lorentzian 3-algebra theory, proposed as a worldvolume description of multiple M2-branes, can be obtained directly from maximally supersymmetric Yang-Mills theory in $2+1$ dimensions via the de Wit–Nicolai–Samtleben (dNS) duality. By promoting the YM coupling to an $SO(8)$ vector and then to scalar fields, the authors realize off-shell $SO(8)$ R-symmetry and superconformal structure and reproduce the Lorentzian 3-algebra action without invoking 3-algebras at the outset; on-shell this theory is equivalent to the original SYM. They discuss gauge-invariant operators, the role of nonlocal fields, and potential four-dimensional dualities, concluding that the Lorentzian 3-algebra construction is, in effect, a reformulation of D2-brane physics rather than a distinct IR fixed point for M2-branes. The paper also contrasts this with other M2-brane proposals and highlights that the IR limit relevant to M2s may emerge only in the infinite-coupling regime, motivating future exploration of genuinely M2-relevant theories such as certain Chern–Simons-matter models.

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.