# Holographic correlators in AdS$_3$

## TL;DR

This paper derives the first holographic four-point correlators of single-trace scalar operators in AdS$_3$/CFT$_2$, using a novel approach that avoids Witten diagrams and leverages heavy-heavy-light-light correlator limits.

## Contribution

It presents the first explicit calculation of holographic four-point correlators of single-trace operators in AdS$_3$, employing a new method based on heavy-light correlator limits and consistency conditions.

## Key findings

- Derived four-point correlators for scalar operators of dimension one in AdS$_3$
- Avoided traditional Witten diagram computations
- Provided new insights into AdS$_3$/CFT$_2$ holography

## Abstract

We derive the four-point correlators of scalar operators of dimension one in the supergravity limit of the D1D5 CFT holographically dual to string theory on AdS$_3\times S^3\times \mathcal{M}$, with $\mathcal{M}$ either $T^4$ or $K3$. We avoid the use of Witten diagrams but deduce our result from a limit of the heavy-heavy-light-light correlators computed in arXiv:1705.09250, together with several consistency requirements of the OPE in the various channels. This result represents the first holographic correlators of single-trace operators computed in AdS$_3$.