Higher Spin N=8 Supergravity

TL;DR

This paper explores the structure of higher spin states in N=8 supergravity within AdS space, connecting boundary singleton theories to bulk supergravity and discussing the embedding of equations of motion.

Contribution

It demonstrates the embedding of N=8 AdS supergravity equations into Vasiliev's higher spin framework and discusses the boundary-bulk correspondence in M-theory context.

Findings

Higher spin states form an infinite tower related to Vasiliev's algebra

Embedding of supergravity equations at linearized level

Speculation on boundary singleton theory capturing bulk dynamics

Abstract

The product of two N=8 supersingletons yields an infinite tower of massless states of higher spin in four dimensional anti de Sitter space. All the states with spin s > 1/2 correspond to generators of Vasiliev's super higher spin algebra shs^E (8|4) which contains the D=4, N=8 anti de Sitter superalgebra OSp(8|4). Gauging the higher spin algebra and introducing a matter multiplet in a quasi-adjoint representation leads to a consistent and fully nonlinear equations of motion as shown sometime ago by Vasiliev. We show the embedding of the N=8 AdS supergravity equations of motion in the full system at the linearized level and discuss the implications for the embedding of the interacting theory. We furthermore speculate that the boundary N=8 singleton field theory yields the dynamics of the N=8 AdS supergravity in the bulk, including all higher spin massless fields, in an unbroken phase of M-theory.