7D Bosonic Higher Spin Theory: Symmetry Algebra and Linearized Constraints

TL;DR

This paper constructs a 7D bosonic higher spin algebra hs(8*) and explores its gauge theory, spectrum, and potential connection to M-theory and holography involving free (2,0) tensor multiplets.

Contribution

It introduces the minimal bosonic higher spin extension of the 7D AdS algebra, detailing its generators, spectrum, and gauge structure, and proposes a link to M-theory on AdS_7×S^4.

Findings

Construction of the hs(8*) algebra with spin s=1,3,5,...

Spectrum includes fields with spin s=0,2,4,... forming a specific unitary irreducible representation

Proposal that the gauge theory describes a truncation of M theory with a holographic dual of free (2,0) tensor multiplets

Abstract

We construct the minimal bosonic higher spin extension of the 7D AdS algebra SO(6,2), which we call hs(8*). The generators, which have spin s=1,3,5,..., are realized as monomials in Grassmann even spinor oscillators. Irreducibility, in the form of tracelessness, is achieved by modding out an infinite dimensional ideal containing the traces. In this a key role is played by the tree bilinear traces which form an SU(2)_K algebra. We show that gauging of hs(8*) yields a spectrum of physical fields with spin s=0,2,4,...which make up a UIR of hs(8*) isomorphic to the symmetric tensor product of two 6D scalar doubletons. The scalar doubleton is the unique SU(2)_K invariant 6D doubleton. The spin s\geq 2 sector comes from an hs(8*)-valued one-form which also contains the auxiliary gauge fields required for writing the curvature constraints in covariant form. The physical spin s=0 field arises in a separate zero-form in a `quasi-adjoint' representation of hs(8*). This zero-form also contains the spin s\geq 2 Weyl tensors, i.e. the curvatures which are non-vanishing on-shell. We suggest that the hs(8*) gauge theory describes the minimal bosonic, massless truncation of M theory on AdS_7\times S^4 in an unbroken phase where the holographic dual is given by N free (2,0) tensor multiplets for large N.