AdS one-loop partition functions from bulk and edge characters

Abstract

We show that the one-loop partition function of any higher spin field in $(d+1)$-dimensional Anti-de Sitter spacetime can be expressed as an integral transform of an $\text{SO}(2,d)$ bulk character and an $\text{SO}(2,d-2)$ edge character. We apply this character integral formula to various higher-spin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters that lead to agreement with the predictions of HS/CFT holography. We also discuss about the relation between the character integral representation and Rindler-AdS thermal partition function.

arXiv comment55 pages

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• Characters, quasinormal modes, and Schwinger pairs in $d{S}_2$ with flux
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• Explicit holography for vector models at finite $N$, volume and temperature
• Quantum Entanglement on Black Hole Horizons in String Theory and Holography
• Partition functions and entanglement entropy: Weyl graviton and conformal higher spin fields
• Sphere free energy of scalar field theories with cubic interactions
• Bulk-boundary entanglement correspondence and the Ryu-Takayanagi conjecture in an $Ad{S}_2/CF{T}_1$ setup
• Massive fields and Wilson spools in JT gravity
• Partition functions of $p$-forms from Harish-Chandra characters
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