Probing higher spin black holes

Abstract

We study the propagation of scalar fields on various backgrounds in three dimensional higher spin gravity. Our main emphasis is on obtaining the bulk-boundary propagator, which can be efficiently computed using group theory and higher spin gauge symmetry and from which we can extract scalar two-point functions in the dual CFT. As an illustration, we obtain a simple closed form expression for the propagator in a particular spin-3 deformation of AdS_3. In the case of higher spin black holes, we prove on general grounds that the propagator respects an imaginary time periodicity consistent with the thermal nature of the black hole; in doing so we make progress in understanding the group exponentiation of the higher spin Lie algebra hs[λ], and its center. We also explicitly compute the propagator in the black hole background at first order in the higher spin charge. Evaluated on the Lorentzian section, the result is consistent with an interpretation in which the black hole has two causally disconnected boundary components, as is the case for the BTZ black hole.

41 pages. v3: corrected typos

References in corpus (7)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Symmetries of Holographic Minimal Models
• Higher Spins in AdS and Twistorial Holography
• Real Forms of Complex Higher Spin Field Equations and New Exact Solutions
• Exploring Three-dimensional Higher-Spin Supergravity based on sl(N |N - 1) Chern-Simons theories
• Supersymmetry of classical solutions in Chern-Simons higher spin supergravity

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• The semiclassical limit of W_N CFTs and Vasiliev theory
• W Symmetry and Integrability of Higher spin black holes
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• Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics
• Matching four-point functions in higher spin AdS_3/CFT_2
• Probing higher spin black holes from CFT
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• Higher Spins and Matter Interacting in Dimension Three
• Three-Point Functions in N=2 Higher-Spin Holography
• A note on conical solutions in 3D Vasiliev theory
• 4D Higher Spin Black Holes with Nonlinear Scalar Fluctuations
• An Entropy Formula for Higher Spin Black Holes via Conical Singularities
• Higher Spin Currents in the N=1 Stringy Coset Minimal Model
• Higher Spin Entanglement Entropy
• On big crunch solutions in Prokushkin-Vasiliev theory
• Eternal Higher Spin Black Holes: a Thermofield Interpretation
• On the partition functions of higher spin black holes
• Field Theory of Primaries in W_N Minimal Models
• A new spin on entanglement entropy
• Higher Spin Lifshitz Theory and Integrable Systems
• Black Holes in the 3D Higher Spin Theory and Their Quasi Normal Modes
• Higher-spin gauge theories in three spacetime dimensions
• Resummation of scalar correlator in higher spin black hole background
• On matter coupled to the higher spin square
• On scalar propagators of three-dimensional higher-spin black holes
• About the phase space of SL(3) Black Holes