On spectrally flowed local vertex operators in AdS3

Abstract

We provide a novel local definition for spectrally flowed vertex operators in the SL(2,R)WZW model, generalising the proposal of [1] for the singly-flowed case to all ω > 1. This allows us to establish the precise connection between the computation of correlators using the so-called spectral flow operator [1], and the methods introduced recently in [2] based on local Ward identities. We show that the auxiliary variable y used by the authors of [2] arises naturally from a point-splitting procedure in the space-time coordinate. The recursion relations satisfied by spectrally flowed correlators, which take the form of partial differential equations in y-space, then correspond to null-state conditions for generalised spectral flowed operators. We highlight the role of certain SL(2,R) discrete module isomorphisms in this context, and prove the validity of the conjecture put forward in [2] for y-space structure constants of three-point functions with arbitrary spectral flow charges.