# AdS$_3$ Holography at Dimension Two

## TL;DR

This paper derives an explicit holographic dictionary for AdS3/CFT2, mapping supergravity solutions to CFT operators of dimension two, and provides tests supporting the duality for supersymmetric black hole microstates.

## Contribution

It constructs the detailed map between supergravity asymptotics and CFT operators of dimension two, including operator mixing, and performs tests validating the holographic correspondence for superstrata.

## Key findings

- Explicit holographic map for dimension (1,1) operators
- Validation of the dual CFT states via precision tests
- Support for superstrata as microstates of black holes

## Abstract

Holography can provide a microscopic interpretation of a gravitational solution as corresponding to a particular CFT state: the asymptotic expansion in gravity encodes the expectation values of operators in the dual CFT state. Such a correspondence is particularly valuable in black hole physics. We study supersymmetric D1-D5-P black holes, for which recently constructed microstate solutions known as "superstrata" provide strong motivation to derive the explicit D1-D5 holographic dictionary for CFT operators of total dimension two. In this work we derive the explicit map between one-point functions of scalar chiral primaries of dimension (1,1) and the asymptotic expansions of families of asymptotically AdS$_3\times$S$^3 \times$M supergravity solutions, with M either T$^4$ or K3. We include all possible mixings between single-trace and multi-trace operators. We perform several tests of the holographic map, including new precision holographic tests of superstrata, that provide strong supporting evidence for the proposed dual CFT states.