Deriving the AdS3 /CFT2 correspondence

Abstract

It was recently argued that string theory on AdS3× S3× 𝕋4 with one unit (k = 1) of NS-NS flux is exactly dual to the symmetric orbifold CFT SymN (𝕋4). In this paper we show how to directly relate the n-point correlators of the two sides to one another. In particular, we argue that the correlators of the world-sheet theory are delta-function- localised in string moduli space to those configurations that allow for a holomorphic covering map of the S2-boundary of AdS3 by the world-sheet. This striking feature can be seen both from a careful Ward identity analysis, as well as from semi-classically exact AdS3 solutions that are pinned to the boundary. The world-sheet correlators therefore have exactly the same structure as in the Lunin-Mathur construction of symmetric orbifold CFT correlators in terms of a covering surface — which now gets identified with the world-sheet. Together with the results of [1, 2] this essentially demonstrates how the k = 1 AdS3 string theory becomes equivalent to the spacetime orbifold CFT in the genus expansion.