Real forms of complex higher spin field equations and new exact solutions

Abstract

We formulate four-dimensional higher spin gauge theories in spacetimes with signature ( 4 − p , p ) and non-vanishing 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 one 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.