7D bosonic higher spin gauge theory: symmetry algebra and linearized constraints Original Research Article

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⩾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⩾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 AdS7×S4 in an unbroken phase where the holographic dual is given by N free (2,0) tensor multiplets for large N.