Towards higher-spin AdS2/CFT1 holography

Abstract

We aim at formulating a higher-spin gravity theory around AdS 2 relevant for holography. As a first step, we investigate its kinematics by identifying the low-dimensional cousins of the standard higher-dimensional structures in higher-spin gravity such as the singleton, the higher-spin symmetry algebra, the higher-rank gauge and matter fields, etc. In particular, the higher-spin algebra is given here by hs[λ] and parameterized by a real parameter λ. The singleton is defined to be a Verma module of the AdS 2 isometry subalgebra so(2, 1) ⊂ hs[λ] with conformal weight ∆ = 1±λ2 . On the one hand, the spectrum of local modes is determined by the Flato-Fronsdal theorem for the tensor product of two such singletons. It is given by an infinite tower of massive scalar fields in AdS 2 with ascending masses expressed in terms of λ. On the other hand, the higher-spin fields arising through the gauging of hs[λ] algebra do not propagate local degrees of freedom. Our analysis of the spectrum suggests that AdS 2 higher-spin gravity is a theory of an infinite collection of massive scalars with fine-tuned masses, interacting with infinitely many topological gauge fields. Finally, we discuss the holographic CFT 1 duals of the kinematical structures identified in the bulk.

AdS3/AdS2 degression of massless particles

“…Since the interacting theory here also remains topological, it is expected that its dimensional degression yields a version of the AdS 2 higher-spin gravity [43][44][45] which describes finitely many massive spinless excitations with higher-spin-gravitational interactions. 8 Another implication of the AdS 3 /AdS 2 degression may be relevant in the context of AdS 2 higher-spin gravity with infinitely many massive spinless excitations governed by the higher-spin algebra hs[λ], where a real parameter λ defines an equidistant mass spectrum [14,47]. The AdS 3 /AdS 2 spectrum suggests that AdS 2 modes may arise in the form of scalar/vector covariant fields which are indistinguishable on-shell but may participate in different types of interactions.…”

Characteristic cohomology and observables in higher spin gravity

“…The general solution applicable to any higher spin (or arbitrary associative) algebra was proposed in [54]. There are a number of such and very similar models in the literature [29,[53][54][55][56][57][58][59][60][61][62].…”

Flat space holography in spin-2 extended dilaton-gravity

“…For BF-theory based on higher-spin gauge symmetry in JT gravity see[51][52][53][54][55][56][57][58] 3. For a non-relativistic 2d dilaton-gravity setup see the recent papers[59][60][61].…”