Free field world-sheet correlators for AdS3

Abstract

We employ the free field realisation of the $$ \mathfrak{psu}{\left(1,1\left|2\right.\right)}_1 $$ psu 1 1 2 1 world-sheet theory to constrain the correlators of string theory on AdS3× S3× 𝕋4 with unit NS-NS flux. In particular, we directly obtain the unusual delta function localisation of these correlators onto branched covers of the boundary S2 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.

Stress-energy tensor correlators from the world-sheet

“…It would be interesting to generalise the analysis of this paper to the supersymmetric theory, in particular using the free field realisation of psu(1, 1|2) 1 that was recently employed JHEP03(2021)036 in [5]. It would also be interesting to use similar techniques to rederive the symmetry algebra of the dual CFT from the world-sheet; this would complement the analysis of [6,8,9], where this was done algebraically.…”

“…where we have only written out the singular terms. They follow from the 'usual' OPE relations 5 at z = x = 0,…”

“…The basic strategy to determine the world-sheet correlators is to use the Ward identities associated to the sl(2, R) k currents. This method was developed for correlators involving only primary states in [3], see also [5] for a generalisation to the free field realisation of psu(1, 1|2) 1 ; this general method will be briefly reviewed in section 3.1. For the application we have in mind we also need to determine the Ward identities for correlators involving descendant states, and we explain in section 3.2 the modifications that are required for that case.…”

“…In recent years we have seen growing evidence for the equivalence between string theory on AdS 3 × S 3 × T 4 with one unit of NS-NS flux (k = 1), and the symmetric orbifold theory of T 4 [1][2][3], see also [4]. In particular, it was shown in [2] that the spectra of the two descriptions agree precisely, and the structure of correlation functions has also been matched [3,5].…”

“…In the supersymmetric case based on psu(1, 1|2)1, it was recently shown in[5] that this is in fact the only solution 11. Since the system of relations of section 3.2 is overcomplete, it is a non-trivial consistency check that a solution exists at all.…”