Higher Spin Gauge Theories: Star-Product and Ads Space

Abstract

We review the theory of higher spin gauge fields in 2+1 and 3+1 dimensional anti-de Sitter space and present some new results on the structure of higher spin currents and explicit solutions of the massless equations. A previously obtained d=3 integrating flow is generalized to d=4 and is shown to give rise to a perturbative solution of the d=4 nonlinear higher spin equations. A particular attention is paid to the relationship between the star-product origin of the higher spin symmetries, AdS geometry and the concept of space-time locality.

Comments on Rényi entropy in AdS3/CFT2

“…This theory can also be supersymmetrized, non-Abelianized, and/or consistently coupled to propagating matter. The latter defines the Vasiliev theories of higher spins [9,33]. The realization of symmetries in this formulation is quite elegant: G × G is identified with the wedge algebra of the CFT, and the asymptotic symmetry of the theory with suitably defined AdS boundary conditions is the extension of G × G beyond the wedge to…”

Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions

“…Various explicit sets of (conformal) conserved currents on Minkowski spacetime were provided in [31][32][33][34]. The symmetric conserved current (4.2) of rank r is bilinear in the scalar field and contains exactly r derivatives.…”

Scalar field corrections to AdS4gravity from higher spin gauge theory

“…Assuming that Φ and W are weak fields, the constraints on A and Φ leading to spacetime dynamics have the following expansion [9,10,18] …”

“…Note that this ensures invariance under higher spin gauge transformations and diffeomorphisms (which are incorporated into the gauge group as field dependent gauge transformations). The rationale behind the expansion of the µ component in (38) is that it implies that the constraints are manifestly invariant under local Lorentz transformations under which the component fields in e and W transform as Lorentz tensors and ω as the Lorentz connection [18,10]. The linearised form of (28) contains the physical field equations for spin s = 2, 4, .…”