# AdS$_3$ four-point functions from $\frac{1}{8}$-BPS states

## TL;DR

This paper computes four-point functions involving all known 1/8-BPS heavy states in AdS3/CFT2, using supergravity solutions and Ward identities, providing new holographic correlators for these operators.

## Contribution

It introduces a method to compute four-point functions of 1/8-BPS states in AdS3/CFT2 without Witten diagrams, utilizing explicit supergravity solutions and symmetry constraints.

## Key findings

- Derived relations among four-point functions using Ward identities.
- Reconstructed all-light four-point functions involving 1/8-BPS operators.
- Provided the first holographic correlators for single-trace 1/8-BPS operators in AdS3.

## Abstract

We compute four-point functions in the Heavy-Heavy-Light-Light limit involving all possible $\frac{1}{8}$-BPS heavy states whose dual supergravity solutions are explicitly known, avoiding the use of Witten diagrams. This is achieved by using the AdS/CFT dictionary of type IIB supergravity on AdS$_3 \times S^3 \times {\cal M}_4$ that maps supersymmetric heavy operators whose conformal dimension is the order of the central charge to explicit asymptotically AdS supergravity solutions. Using the Ward Identities for the generators of the ${\cal N}=(4,4)$ superconformal $SU(2)$ Kac-Moody algebra, we can relate all of these four-point functions to each other and to other known four-point functions involving $\frac{1}{4}$-BPS heavy states, furnishing non-trivial checks of the computations. Finally, the Ward Identities can be employed to reconstruct the all-light four-point functions, providing the first holographic correlators of single-trace operators computed in AdS$_3$ involving $\frac{1}{8}$-BPS operators.