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.

27 pages, 2 appendices; v2: Reference added, fixed minor typo in arxiv abstract

References in corpus (13)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Comments on the Bagger-Lambert theory and multiple M2-branes
• M2 to D2
• n-ary algebras: a review with applications
• Membranes on an Orbifold
• M2-branes, 3-Lie Algebras and Plucker relations
• N=4 SYM on R x S^3 and Theories with 16 Supercharges
• Light-cone M5 and multiple M2-branes
• SDiff Gauge Theory and the M2 Condensate

Cited by in corpus (5)

• Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory
• Exact correlators in the Gaussian Hermitian matrix model
• $W_{1+\infty }$ constraints for the hermitian one-matrix model
• Reviving 3D $\mathcal{N}=8$ superconformal field theories
• On matter coupled to the higher spin square