Free field world-sheet correlators for AdS3
Andrea Dei, Matthias R. Gaberdiel, Rajesh Gopakumar, Bob Knighton
Abstract
A bstract We employ the free field realisation of the $$ \mathfrak{psu}{\left(1,1\left|2\right.\right)}_1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>psu</mml:mi> <mml:msub> <mml:mfenced> <mml:mn>1</mml:mn> <mml:mrow> <mml:mn>1</mml:mn> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> </mml:mrow> </mml:mfenced> <mml:mn>1</mml:mn> </mml:msub> </mml:math> world-sheet theory to constrain the correlators of string theory on AdS 3 × S 3 × 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 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.