Free field world-sheet correlators for ${\rm AdS}_3$

TL;DR

This paper uses free field techniques to compute and understand world-sheet correlators in string theory on AdS3, revealing their localization properties and connection to symmetric orbifold duals.

Contribution

It introduces a novel approach employing free field realization to derive correlators and demonstrates their localization onto branched covers, clarifying the AdS3/CFT2 correspondence.

Findings

Correlators localize on branched covers of the boundary sphere.

The approach reveals a twistorial structure in the correlators.

Explicit computations confirm the theoretical predictions.

Abstract

We employ the free field realisation of the $\mathfrak{psu}(1,1|2)_1$ world-sheet theory to constrain the correlators of string theory on ${\rm AdS}_3\times {\rm S}^3\times \mathbb{T}^4$ with unit NS-NS flux. In particular, we directly obtain the unusual delta function localisation of these correlators onto branched covers of the boundary ${\rm S}^2$ by the (genus zero) world-sheet -- this is the key property which makes the equivalence to the dual symmetric orbifold manifest. In our approach, this feature follows from a remarkable `incidence relation' obeyed by the correlators, which is reminiscent of a twistorial string description. We also illustrate our results with explicit computations in various special cases.