Superconformal M2-branes and generalized Jordan triple systems

TL;DR

This paper proposes a new mathematical framework using generalized Jordan triple systems to describe M2-branes in three-dimensional superconformal theories, extending previous algebraic approaches and unifying theories with different supersymmetries.

Contribution

It introduces a novel connection between superconformal M2-brane theories and generalized Jordan triple systems, expanding the algebraic structures used in M-theory models.

Findings

The theory with six supersymmetries is expressed via graded Lie algebras.

The approach includes the BLG theory with eight supersymmetries as a special case.

The structure constants relate directly to the algebraic framework proposed.

Abstract

Three-dimensional conformal theories with six supersymmetries and SU(4) R-symmetry describing stacks of M2-branes are here proposed to be related to generalized Jordan triple systems. Writing the four-index structure constants in an appropriate form, the Chern-Simons part of the action immediately suggests a connection to such triple systems. In contrast to the previously considered three-algebras, the additional structure of a generalized Jordan triple system is associated to a graded Lie algebra, which corresponds to an extension of the gauge group. In this note we show that the whole theory with six manifest supersymmetries can be naturally expressed in terms of such a graded Lie algebra. Also the BLG theory with eight supersymmetries is included as a special case.