Holographic One-Point Function and Geodesics in SdS$_3$

TL;DR

This paper extends the holographic relation between boundary one-point functions and geodesic lengths from AdS/CFT to three-dimensional Schwarzschild-de Sitter spacetimes, demonstrating a similar encoding of geodesic information.

Contribution

It establishes an analogous holographic correspondence for SdS$_3$, relating thermal one-point functions to complex geodesic lengths, generalizing previous AdS/CFT results.

Findings

Proves the correspondence for SdS$_3$ with finite orbifold group.

Shows the boundary one-point function encodes geodesic length to the black hole singularity.

Identifies a suitable bulk-boundary kernel for the SdS$_3$ case.

Abstract

Grinberg-Maldacena showed that, for AdS/CFT, the thermal one-point function of a heavy boundary operator in the dual conformal field theory encodes the complex geodesic length from the boundary insertion to the black hole singularity. We show that for an appropriate choice of bulk-boundary kernel, an analogous result holds for three-dimensional Schwarzschild-de Sitter black hole. We prove the result for the case where SdS$_3$ has a finite orbifold group.