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

TL;DR

This paper investigates the locality properties of higher-spin gravity in (A)dS_4, demonstrating that it is local in Euclidean signatures and suggesting similar locality in Lorentzian de Sitter space, contrasting previous non-locality claims.

Contribution

The study shows that higher-spin gravity is local at distances greater than the curvature radius in Euclidean (A)dS, challenging prior non-locality assertions based on Lorentzian boundary limits.

Findings

Higher-spin theory is local in Euclidean (A)dS at large distances.

Non-locality arguments depend on Lorentzian boundary assumptions.

Euclidean analysis indicates absence of massless exchange non-localities.

Abstract

We consider higher-spin gravity in (A)dS_4, 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.