Towards Massless Higher Spin Extension of D=5, N=8 Gauged Supergravity

TL;DR

This work constructs a massless higher spin extension hs$(2,2|4)$ of the AdS$_5$ superalgebra PSU$(2,2|4)$ and gauges it in five dimensions. The physical spectrum is identified as the symmetric product of two AdS$_5$ N=4 SYM doubletons, organized into levels $\ell=0,1,\dots$, with the D=5, N=8 supergravity multiplet emerging at $\ell=0$; a master gauge field $[A]$ and a master scalar field $\Phi$ encode all higher-spin states, whose linearized constraints yield the full spectrum of massless fields, including self-dual 2-form potentials and their higher-spin generalizations. The linearized equations reproduce the D=5, N=8 gauged supergravity dynamics and generalize to higher spins with dualization patterns that relate one-forms and two-forms across the spectrum. These results provide a concrete framework for a possible interacting higher spin theory in AdS$_5$, with implications for tensionless string limits and a bulk dual to the free limit of $\mathcal{N}=4$ SYM. The paper lays out the algebraic construction, the master-field content, and the linearized dynamics, setting the stage for future work on full interactions and holographic connections.

Abstract

The AdS_5 superalgebra PSU(2,2|4) has an infinite dimensional extension, which we denote by hs(2,2|4). We show that the gauging of hs(2,2|4) gives rise to a spectrum of physical massless fields which coincides with the symmetric tensor product of two AdS_5 spin-1 doubletons (i.e. the N=4 SYM multiplets living on the boundary of AdS_5). This product decomposes into levels \ell=0,1,2,..,\infty of massless supermultiplets of PSU(2,2|4). In particular, the D=5, N=8 supergravity multiplet arises at level \ell=0. In addition to a master gauge field, we construct a master scalar field containing the s=0,1/2 fields, the anti-symmetric tensor field of the gauged supergravity and its higher spin analogs. We define the linearized constraints and obtain the linearized field equations of the full spectrum, including those of D=5,N=8 gauged supergravity and in particular the self-duality equations for the 2-form potentials of the gauged supergravity (forming a 6-plet of SU(4)), and their higher spin cousins with s=2,3,...,\infty.