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

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 ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathbb{T}}^4$ with unit NS-NS flux. In particular, we directly obtain the unusual delta function localisation of these correlators onto branched covers of the boundary ${\mathrm{S}}^2$ 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.

42 pages