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

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 greater than or equal to 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 greater than or equal to 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) x (S)4 in an unbroken phase where the holographic dual is given by N free (2, 0) tensor multiplets for large N. (C) 2002 Elsevier Science B.V. All rights reserved.