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

TL;DR

This paper explores the holographic duality between 4d higher-spin gravity and a 3d free vector model, revealing that boundary correlator calculations challenge traditional locality assumptions and help resolve issues in higher-spin dS/CFT.

Contribution

It introduces a novel method of evaluating boundary correlators using HS-algebraic twistorial expressions on entire source distributions, and addresses the conflict between boundary locality and higher-spin symmetry.

Findings

Disagreement between HS partition function and CFT due to contact corrections persists.

Boundary locality conflicts with HS symmetry, leading to a choice to prioritize HS symmetry.

Resolving this conflict clarifies the structure of higher-spin dS/CFT and recovers the form of Z_HS from first principles.

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.