# Free field world-sheet correlators for AdS_3

Andrea Dei, Matthias R. Gaberdiel, Rajesh Gopakumar, Bob Knighton

Andrea Dei, Matthias R. Gaberdiel, Rajesh Gopakumar, Bob Knighton

**23/9/20**Published in : arXiv:2009.11306

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.