# Holographic correlators in AdS$_3$ without Witten diagrams

## TL;DR

This paper derives a compact formula for holographic 4-point correlators in AdS3 x S3, using supergravity results and Mellin space techniques, avoiding traditional Witten diagram calculations.

## Contribution

It introduces a novel Mellin space approach to compute holographic correlators in AdS3 without relying on Witten diagrams, providing a conjectured complete formula.

## Key findings

- Derived a formula for 4-point correlators in AdS3 x S3.
- Rewrote s-channel results in Mellin space for compactness.
- Proposed a conjecture for the full correlator expression.

## Abstract

We present a formula for the holographic 4-point correlators in AdS$_3 \times S^3$ involving four single-trace operators of dimension $k, k, l, l$. As an input we use the supergravity results for the Heavy-Heavy-Light-Light correlators that can be derived by studying the linear fluctuations around known asymptotically AdS$_3 \times S^3$ geometries. When the operators of dimension $k$ and $l$ are in the same multiplet there are contributions due to the exchange of single-trace operators in the $t$ and $u$ channels, which are not captured by the approach mentioned above. However by rewriting the $s$-channel results in Mellin space we obtain a compact expression for the $s$-channel contribution that makes it possible to conjecture a formula for the complete result. We discuss some consistency checks that our proposal meets.