Notes on gravity multiplet correlators in $AdS_3 \times S^3$

TL;DR

This paper derives a compact Mellin space formula for four-point holographic correlators in AdS3 x S3 supergravity, revealing new insights into their structure and limits, including flat-space and R-symmetry violations.

Contribution

It introduces a novel compact Mellin space expression for four-point correlators in AdS3 x S3 supergravity, utilizing a hidden six-dimensional conformal symmetry.

Findings

Derived a compact Mellin space formula for correlators

Analyzed various limits including flat-space and R-symmetry

Revealed structural properties of correlators in supergravity

Abstract

We present a compact formula in Mellin space for the four-point tree-level holographic correlators of chiral primary operators of arbitrary conformal weights in $(2,0)$ supergravity on $AdS_3 \times S^3$, with two operators in tensor multiplet and the other two in gravity multiplet. This is achieved by solving the recursion relation arising from a hidden six-dimensional conformal symmetry. We note the compact expression is obtained after carefully analysing the analytic structures of the correlators. Various limits of the correlators are studied, including the maximally R-symmetry violating limit and flat-space limit.