Higher Spin N=8 Supergravity in AdS_4

TL;DR

This paper reviews the structure of higher spin N=8 supergravity in four-dimensional AdS space, connecting it to singleton theories and M-theory limits, and discusses its algebraic foundations and physical implications.

Contribution

It provides a detailed review of the higher spin extension of N=8 AdS supergravity, including its algebraic structure and relation to singleton theories and M-theory.

Findings

The theory is constructed via gauging the shs^E(8|4) superalgebra.

Physical states correspond to symmetric products of OSp(8|4) singletons.

The supergravity theory is linked to the supermembrane limit of M-theory.

Abstract

We review the basic structure of the higher spin extension of D=4, N=8 AdS supergravity. The theory is obtained by gauging the higher spin superalgebra shs^E(8|4) by a procedure pioneered by Vasiliev. The algebra shs^E(8|4) is a subalgebra of the enveloping algebra of OSp(8|4). The physical states of the theory are in one to one correspondence with the symmetric product of two OSp(8|4) singletons. This singleton theory, which may be viewed in a certain limit as the supermembrane theory on AdS_4 x S^7, is expected to describe the dynamics of the higher spin theory. Thus, the higher spin N=8 supergravity on AdS_4 is conjectured to describe the field theory limit of M-theory on AdS_4 x S^7.