Higher Spin N=8 Supergravity

TL;DR

The paper shows that the symmetric product of two $N=8$ supersingletons yields an infinite tower of massless higher spin states in AdS$_4$, with spins $s\ge1$ described by Vasiliev's HS superalgebra $shs^E(8|4)$ that contains the $D=4$, $N=8$ AdS superalgebra $OSp(8|4)$. It constructs nonlinear equations via gauging of the HS algebra with a quasi-adjoint matter multiplet, formulates an extended FDA with extra $Z$-variables, and demonstrates that the linearized HS system embeds the linearized $N=8$ AdS supergravity, including its full multiplet content. The analysis yields a precise relation between the HS and gravitational couplings, $\frac{g^2}{\kappa^2}=\frac{1}{2}\lambda^2$, and shows that the $k=0$ sector reproduces the known supergravity spectrum. The authors speculate that the boundary $N=8$ singleton theory may encode the bulk HS dynamics in an unbroken M-theory phase, hinting at a bulk/boundary duality framework for HS theories and their relation to M-theory and hidden symmetries such as $E_7$. The work provides a robust linearized bridge between HS gauge theories and conventional gauged supergravity, paving the way for exploring nonlinear interactions and holographic interpretations of higher spin AdS supergravity.

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.

Figures (1)

• Figure 1: Each entry of the integer grid, $m,n=0,1,2,...$, represents a component $\omega(m,n;\theta\,)$ of the $shs^E(8|4)$ valued connection one form $\omega$ according to the following rule: the $\star$ denote the spin $s=1$ component; a $\bullet$ denotes a generalized vierbein; a $\circ$ denotes a generalized gravitino; a $\diamondsuit$ denotes an auxiliary generalized Lorentz connection and the $\times$'s denote the remaining auxiliary connections.