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 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.

One-loop effective actions and higher spins. Part II

“…Other topics, such as the discussion of the ambiguities inherent in the choice of the conserved currents in the initial matter model, will be included in a subsequent article. This is a good point to mention that our research is indebted to several preexisting works, in particular with [17][18][19] as far as the inspiration is concerned, with [20][21][22][23][24][25][26][27][28][29] as far as the methods are concerned and with [4,5,[30][31][32][33][34][35][36][37][38][39][40][41] for HS theories. Other papers of ours, related to the present one are, beside [1,42,43].…”

“…On the other hand, we have significant higher spin results: free fields can be constructed in the same manner as in lower spin cases (see, e.g. [49]); a few cubic interaction terms have been constructed in the literature (see [31][32][33][34][35][36][37][38]); most notably, a full consistent covariant HS theory in AdS background has been constructed by Vasilev and collaborators [50][51][52][53]. In our previous paper, [1], we remarked that free lower spin field theories possess conserved higher spin currents which simply "beg" to be coupled to higher spin fields.…”

Massive fermion model in 3d and higher spin currents

“…In the literature one can find two kinds of generalizations of the CS action in 3d to higher spins (for a general review on higher spin theories, see [25][26][27][28][29][30][31][32]). One leads to quadratic equations of motion, the other to higher derivative equations of motion.…”

Supersymmetric holography on AdS3

“…Returning to the limit of theory of (2.13), it was proposed in [29] that the Hilbert space reproducing the partition function of the dual AdS 3 theory in the limit (2.15) is 16) where the two pairs of Young diagrams Λ = (Λ l , Λ r ) and Ξ = (Ξ l , Ξ r ) label representations…”

“…About ten years ago it was conjectured by Klebanov & Polyakov [11] (see also [12] for a subsequent refinement) that a specific higher spin theory on AdS 4 [13] (see for example [14,15,16,17] for reviews) is dual to the large N limit of the O(N ) vector model in 3 dimensions; actually, there are four different versions of this duality, depending on whether one considers the free or interacting O(N ) theory, and whether it is based on fermions or bosons. During the last two years, highly nontrivial evidence in favour of this conjecture has been found.…”