Towards higher-spin AdS${}_2$/CFT${}_1$ 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 $hs[\lambda ]$ and parameterized by a real parameter $\lambda$. The singleton is defined to be a Verma module of the AdS${}_2$ isometry subalgebra $so(2,1)\subset hs[\lambda ]$ with conformal weight $\Delta =\frac{1\pm \lambda }{2}$. 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 $\lambda$. On the other hand, the higher-spin fields arising through the gauging of $hs[\lambda ]$ 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.

49 pages, v2: Self-contained Section 8 about higher-spin BF actions removed, to be restored as a forthcoming independent manuscript. All results unaffected. Minor corrections. v3: More explanations and comments, typos corrected, references added. Journal version

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• Near Conformal Perturbation Theory in SYK Type Models
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• Higher spin JT gravity and a matrix model dual
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Schwarzian for colored Jackiw-Teitelboim gravity
• Color decorations of Jackiw-Teitelboim gravity
• Higher spin wormholes from modular bootstrap
• Target space diffeomorphisms in Poisson sigma models and asymptotic symmetries in 2D dilaton gravities