Looking for a bulk point

TL;DR

This paper investigates the nature of singularities in Lorentzian correlators within theories with gravity duals, demonstrating that certain bulk-specific singularities serve as diagnostics of bulk locality and are absent in the exact nonperturbative theory.

Contribution

It introduces a distinction between boundary and bulk Landau diagram singularities and proves the absence of certain singularities in 1+1 dimensional CFTs nonperturbatively.

Findings

Bulk Landau diagram singularities indicate bulk locality.

Perturbative singularities differ from nonperturbative behavior.

In 1+1 dimensions, certain singularities are proven to be absent nonperturbatively.

Abstract

We consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these singularities are a clear diagnostic of bulk locality. We analyze some properties of these perturbative singularities and discuss their relation to the OPE and the dimensions of double-trace operators. In the exact nonperturbative theory, we expect no singularity at these locations. We prove this statement in 1+1 dimensions by CFT methods.