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

TL;DR

This paper develops four-dimensional higher spin gauge theories in various spacetime signatures with a cosmological constant, discovering new exact solutions including higher spin generalizations of gravitational instantons and solutions with non-vanishing massless higher spin fields.

Contribution

It formulates higher spin gauge theories in diverse signatures and finds the first exact 4D solutions with non-vanishing massless higher spin fields, including instanton-like solutions.

Findings

Found SO(4-p,p) invariant deformations with continuous and discrete parameters.

Discovered non-maximally symmetric solutions with vanishing Weyl tensors.

Constructed higher spin generalizations of Type D gravitational instantons.

Abstract

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.