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

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

2007-06-20

arxiv.org/abs/0706.2983v1

Nucl.Phys.B791:231-264,2008

Physics

High Energy Physics

High Energy Physics - Theory

40 pages, latex

Scientific paper

10.1016/j.nuclphysb.2007.08.002

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.

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