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

TL;DR

This paper develops a framework for extending D=5, N=8 gauged supergravity to include an infinite spectrum of massless higher spin fields by gauging an infinite-dimensional superalgebra, revealing a rich structure of supermultiplets.

Contribution

It introduces a massless higher spin extension of D=5, N=8 gauged supergravity via the gauging of the hs(2,2|4) superalgebra, and constructs the corresponding spectrum and field equations.

Findings

Spectrum matches symmetric tensor product of boundary N=4 SYM multiplets

Constructs master gauge and scalar fields including higher spin fields

Derives linearized field equations and self-duality conditions for the extended spectrum

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.