Higher spins from Nambu-Chern-Simons theory

TL;DR

This paper introduces a novel higher spin gravity theory in three dimensions based on Nambu-Chern-Simons action, featuring a simple gauge group and extending the understanding of higher spin interactions and supersymmetric models.

Contribution

It proposes a new Nambu-Chern-Simons formulation for higher spin gravity with a simple gauge group, contrasting with previous models, and analyzes supersymmetric M2 brane configurations and gauge group topology.

Findings

Defined a Nambu-Chern-Simons action for higher spin gravity.

Identified the gauge group as simple, unlike previous models.

Classified instantons and computed the homotopy type of the gauge group.

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.