On Exact Solutions and Perturbative Schemes in Higher Spin Theory

Abstract

Abstract:We review various methods for finding exact solutions of higher spin theory in four dimensions, and survey the known exact solutions of (non)minimal Vasiliev's equations. These include instanton-like and black hole-like solutions in (A)dS and Kleinian spacetimes. A perturbative construction of solutions with the symmetries of a domain wall is also described. Furthermore, we review two proposed perturbative schemes: one based on perturbative treatment of the twistor space field equations followed by inverting Fronsdal kinetic terms using standard Green's functions; and an alternative scheme based on solving the twistor space field equations exactly followed by introducing the spacetime dependence using perturbatively defined gauge functions. Motivated by the need to provide a higher spin invariant characterization of the exact solutions, aspects of a proposal for a geometric description of Vasiliev's equation involving an infinite dimensional generalization of anti de Sitter space are revisited and improved.

FRW and domain walls in higher spin gravity

“…12 As is well-known, upon representing Wigner's deformed oscillators sα in a Fock space for the undeformed oscillators zα, singular vectors appear for an infinite number of discrete critical values of bν; for a brief review and references to original works, see [19]. It would be interesting to study the behaviour of the master fields close to these critical points, which we leave for a future study.…”

“…11 Note that this ansatz for A ′ α is holomorphic in z, and hence the terminology of holomorphic gauge; see [19] for a review. 12 As is well-known, upon representing Wigner's deformed oscillators sα in a Fock space for the undeformed oscillators zα, singular vectors appear for an infinite number of discrete critical values of bν; for a brief review and references to original works, see [19].…”

“…If the dependence of the graviton two-point function deviates from the H 2 /M 2 pl behavior significantly, this scale will change accordingly. 19 In particular, the amplitude of the two-point function of massless graviton (tensor mode) fluctuations should be smaller than ∼ 10 −11 . If the two-point function is similar to that of standard inflation, which goes as H 2 /M JHEP03(2018)153…”

“…In this paper, we shall use a solution generating technique [17][18][19] to build g 6 -invariant solutions to Vasiliev's bosonic theory with non-vanishing (positive or negative) cosmological constant from gauge functions, representing large gauge transformations that alter the asymptotics of the gauge fields, and g 6 -invariant scalar field profiles in the maximally symmetric background. Solutions of Vasiliev's equations with g 3 , g 4 and g 6 symmetries, which are subgroups of the AdS 4 symmetry group, were constructed only at the linearized level in [14] (see [19] for a review) by using a different technique.…”

“…Solutions of Vasiliev's equations with g 3 , g 4 and g 6 symmetries, which are subgroups of the AdS 4 symmetry group, were constructed only at the linearized level in [14] (see [19] for a review) by using a different technique. The fully non-linear solutions presented in this paper are instead obtained by using a different method based on a holomorphic factorization ansatz, and in what we refer to as the holomorphic and L-gauges, described in section 3.…”