Superspace Formulation of 4D Higher Spin Gauge Theory

Interacting AdS_4 higher spin gauge theories with N \geq 1 supersymmetry so far have been formulated as constrained systems of differential forms living in a twistor extension of 4D spacetime. Here we formulate the minimal N=1 theory in superspace, leaving the internal twistor space intact. Remarkably, the superspace constraints have the same form as those defining the theory in ordinary spacetime. This construction generalizes straightforwardly to higher spin gauge theories N>1 supersymmetry.Comment: 24 p

Real Forms of Complex Higher Spin Field Equations and New Exact Solutions

We formulate four dimensional higher spin gauge theories in spacetimes with signature (4-p,p) and nonvanishing cosmological constant. Among them are chiral models in Euclidean (4,0) and Kleinian (2,2) signature involving half-flat gauge fields. Apart from the maximally symmetric solutions, including de Sitter spacetime, we find: (a) SO(4-p,p) invariant deformations, depending on a continuous and infinitely many discrete parameters, including a degenerate metric of rank one; (b) non-maximally symmetric solutions with vanishing Weyl tensors and higher spin gauge fields, that differ from the maximally symmetric solutions in the auxiliary field sector; and (c) solutions of the chiral models furnishing higher spin generalizations of Type D gravitational instantons, with an infinite tower of Weyl tensors proportional to totally symmetric products of two principal spinors. These are apparently the first exact 4D solutions with non-vanishing massless higher spin fields.Comment: 40 pages, late

Scalar Field Corrections to AdS_4 Gravity from Higher Spin Gauge Theory

We compute the complete contribution to the stress-energy tensor in the minimal bosonic higher spin theory in D=4 that is quadratic in the scalar field. We find arbitrarily high derivative terms, and that the total sign of the stress-energy tensor depends on the parity of the scalar field.Comment: 15 pages + appendix (30 pages

Analysis of Higher Spin Field Equations in Four Dimensions

The minimal bosonic higher spin gauge theory in four dimensions contains massless particles of spin s=0,2,4,.. that arise in the symmetric product of two spin 0 singletons. It is based on an infinite dimensional extension of the AdS_4 algebra a la Vasiliev. We derive an expansion scheme in which the gravitational gauge fields are treated exactly and the gravitational curvatures and the higher spin gauge fields as weak perturbations. We also give the details of an explicit iteration procedure for obtaining the field equations to arbitrary order in curvatures. In particular, we highlight the structure of all the quadratic terms in the field equations.Comment: Latex, 30 pages, several clarifications and few references adde

Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings

The correspondences proposed previously between higher spin gauge theories and free singleton field theories were recently extended into a more complete picture by Klebanov and Polyakov in the case of the minimal bosonic theory in D=4 to include the strongly coupled fixed point of the 3d O(N) vector model. Here we propose an N=1 supersymmetric version of this picture. We also elaborate on the role of parity in constraining the bulk interactions, and in distinguishing two minimal bosonic models obtained as two different consistent truncations of the minimal N=1 model that retain the scalar or the pseudo-scalar field. We refer to these models as the Type A and Type B models, respectively, and conjecture that the latter is holographically dual to the 3d Gross-Neveu model. In the case of the Type A model, we show the vanishing of the three-scalar amplitude with regular boundary conditions. This agrees with the O(N) vector model computation of Petkou, thereby providing a non-trivial test of the Klebanov-Polyakov conjecture.Comment: 30p