Higher-spin symmetry vs. boundary locality, and a rehabilitation of dS/CFT

Abstract

We consider the holographic duality between 4d type-A higher-spin gravity and a 3d free vector model. It is known that the Feynman diagrams for boundary correlators can be encapsulated in an HS-algebraic twistorial expression. This expression can be evaluated not just on separate boundary insertions, but on entire finite source distributions. We do so for the first time, and find that the result Z_HS disagrees with the usual CFT partition function. While such disagreement was expected due to contact corrections, it persists even in their absence. We ascribe it to a confusion between on-shell and off-shell boundary calculations. In Lorentzian boundary signature, this manifests via wrong relative signs for Feynman diagrams with different permutations of the source points. In Euclidean, the signs are instead ambiguous, spoiling would-be linear superpositions. Framing the situation as a conflict between boundary locality and HS symmetry, we sacrifice locality and choose to take Z_HS seriously. We are rewarded by the dissolution of a long-standing pathology in higher-spin dS/CFT. Though we lose the connection to the local CFT, the precise form of Z_HS can be recovered from first principles, by demanding a spin-local boundary action.

arXiv comment72 pages; v2: corrected chronology of the references on bulk non-locality

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• Spin-Locality of ${\eta }^2$ and ${\bar{\eta }}^2$ Quartic Higher-Spin Vertices
• Manifest Form of the Spin-Local Higher-Spin Vertex ${{\rm Y}}_{\omega CCC}^{\eta \eta }$
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• Planar solutions of higher-spin theory I: free field level
• Wavefunctions in dS/CFT revisited: principal series and double-trace deformations
• Higher-spin gravity's "string": new gauge and proof of holographic duality for the linearized Didenko-Vasiliev solution
• Bulk locality and gauge invariance for boundary-bilocal cubic correlators in higher-spin gravity