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.

arXiv comment49 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

References in corpus (40)

• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• AdS/CFT Correspondence and Symmetry Breaking
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• An AdS_3 Dual for Minimal Model CFTs
• Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• Bi-Local Holography in the SYK Model
• All point correlation functions in SYK
• On the uniqueness of higher-spin symmetries in AdS and CFT
• Large-N Collective Fields and Holography
• Higher Spin Superalgebras in any Dimension and their Representations
• Character Formulae and Partition Functions in Higher Dimensional Conformal Field Theory
• A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
• A line of CFTs: from generalized free fields to SYK
• Free box^k Scalar Conformal Field Theory
• Towards a bulk description of higher spin SYK
• The continuous spin limit of higher spin field equations
• Masslessness in $n$-dimensions
• New Conformal Higher Spin Gravities in $3d$
• Continuous spin fields of mixed-symmetry type
• Flato-Fronsdal theorem for higher-order singletons
• Continuous-spin field propagator and interaction with matter
• Notes on higher-spin algebras: minimal representations and structure constants
• From Coxeter Higher-Spin Theories to Strings and Tensor Models
• Formal Higher Spin Gravities
• Mixed-symmetry tensor conserved currents and AdS/CFT correspondence
• Uniformizing higher-spin equations
• On Casimir's Ghost
• Anti-de Sitter holography for gravity and higher spin theories in two dimensions
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• Massive fields in AdS(3) and compactification in AdS spacetime
• On higher spin extension of the Jackiw-Teitelboim gravity model
• Unified formulation for helicity and continuous spin fermionic fields
• Massless conformal fields, AdS_{d+1}/CFT_d higher spin algebras and their deformations
• Higher-Spin Gauge Interactions for Matter Fields in Two Dimensions
• Global and local properties of AdS(2) higher spin gravity
• On Dimensional Degression in AdS(d)
• $Ad{S}_2$ holography is (non-)trivial for (non-)constant dilaton
• Twisted Flato-Fronsdal Theorem for Higher-Spin Algebras

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• Color decorations of Jackiw-Teitelboim gravity
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