Quartic locality of higher-spin gravity in de Sitter and Euclidean anti-de Sitter space

We consider higher-spin gravity in (A)dS4, defined as the holographic dual of a free O (N) or Sp(N) vector model. At the quartic level, this theory has been judged non-local at distances greater than the (A)dS radius, due to a mismatch of massless (twist=1) exchange-type terms in its boundary OPE behavior. We review the non-locality argument, and note that it relies on a double-lightcone limit, which requires a Lorentzian boundary. In the Euclidean OPE limit, we demonstrate the absence of massless exchange-type non-localities of any spin, by inspecting a known formula for the bulk exchange diagrams in Euclidean AdS, and constructing upper bounds in which the spin-dependence factorizes from the position-dependence. Our results suggest that higher-spin theory is local (at distances greater than the curvature radius) in spacetimes with Euclidean boundary signature. For Lorentzian bulk, this implies locality in de Sitter space, as opposed to anti-de Sitter.& COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.

Automated summary

This article investigates the higher-spin gravity in (A)dS4 space, which is defined as the holographic dual of a free O(N) or Sp(N) vector model. The theory is considered non-local at distances greater than the (A)dS radius due to a mismatch in the massless exchange terms. However, the study shows that in the Euclidean OPE limit, there are no massless exchange-type non-localities for any spin, suggesting that the higher-spin theory is local in spacetimes with Euclidean boundary signature. This implies locality in de Sitter space for Lorentzian bulk.