Mass-deformed BLG theory in light-cone superspace

Abstract

Maximally supersymmetric mass deformation of the Bagger–Lambert–Gustavsson (BLG) theory corresponds to a non-central extension of the d = 3 N = 8 Poincaré superalgebra (allowed in three dimensions). We obtain its light-cone superspace formulation which has a novel feature of the dynamical supersymmetry generators being cubic in the kinematical ones. The mass deformation picks a quaternionic direction, described by Ωmn, which breaks the SO(8) R-symmetry down to SO(4) × SO(4). The Hamiltonian of the theory is shown to be a quadratic form of the dynamical supersymmetry transformations to all orders in the mass parameter, M, and the structure constants, fabcd.