Modeling Multiple M2's

TL;DR

The paper proposes a non-associative, three-algebra framework for the transverse coordinates of N M2-branes ending on an M5, and derives a cubic supersymmetry structure with a triple product that leads to a novel gauge symmetry. A three-dimensional N=2 superspace Lagrangian is constructed to describe the scalar-spinor sector, with a Basu-Harvey-type BPS funnel emerging from the BPS equations and energy bounds. A concrete non-associative algebra realization is presented to connect the Basu-Harvey dynamics to the M2-M5 intersection, while acknowledging that the full high-symmetry theory remains elusive. The work highlights a path toward incorporating non-associative algebras in M2-brane dynamics and targets future development of a fully SO(8)-invariant description with appropriate gauge structure.

Abstract

We investigate the worldvolume theory that describes N coincident M2-branes ending on an M5 brane. We argue that the fields that describe the transverse spacetime coordinates take values in a non-associative algebra. We postulate a set of supersymmetry transformations and find that they close into a novel gauge symmetry. We propose a three-dimensional N=2 supersymmetric action to describe the truncation of the full theory to the scalar and spinor fields, and show how a Basu-Harvey fuzzy funnel arises as the BPS solution to this theory.