Superconformal M2-branes and generalized Jordan triple systems

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.Comment: 15 pages, v2 and v3: minor corrections and clarifications, references added, v2: section 4 extended, v3: published versio

Duality Symmetries and G^{+++} Theories

We show that the non-linear realisations of all the very extended algebras G^{+++}, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories. This result also holds for G_2^{+++} and we argue that the non-linear realisation of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory. We also find a simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables corrected, other minor changes, one appendix added, refs. added. Version published in Class. Quant. Gra