Stress tensor correlators in three-dimensional gravity

TL;DR

This work tests flat space holography in three dimensions by computing arbitrary connected boundary stress-tensor correlators holographically in 3D Einstein gravity and matching them to 2D Galilean conformal field theory (GCFT$_2$) Ward identities. It develops and utilizes recursion relations derived from Ward identities, both in AdS$_3$/CFT$_2$ via the Chern–Simons formulation and in flat space, to determine all $n$-point correlators, obtaining explicit 2-, 3-, 4-, and 5-point results. The central charges are found to satisfy $c_L=0$ and $c_M=12k=3/G_N$, and the flat space results agree with GCFT predictions, confirming the consistency of flat space holography in 3D. The methodology provides a framework to extend these checks to other 3D gravity theories and holographic setups.

Abstract

We calculate holographically arbitrary n-point correlators of the boundary stress tensor in three-dimensional Einstein gravity with negative or vanishing cosmological constant. We provide explicit expressions up to 5-point (connected) correlators and show consistency with the Galilean conformal field theory Ward identities and recursion relations of correlators, which we derive. This provides a novel check of flat space holography in three dimensions.