Higher spins from Nambu-Chern-Simons theory

Abstract

We propose a new theory of higher spin gravity in three spacetime dimensions. This is defined by what we will call a Nambu-Chern-Simons (NCS) action; this is to a Nambu 3-algebra as an ordinary Chern-Simons (CS) action is to a Lie (2-)algebra. The novelty is that the gauge group of this theory is simple; this stands in contrast to previously understood interacting 3D higher spin theories in the frame-like formalism. We also consider the $N=8$ supersymmetric NCS-matter model (BLG theory), where the NCS action originated: Its fully supersymmetric M2 brane configurations are interpreted as Hopf fibrations, the homotopy type of the (infinite) gauge group is calculated and its instantons are classified.