Superconformal M2-branes and generalized Jordan triple systems

Understand

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.