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On spectrally flowed local vertex operators in AdS$_3$

by Sergio Iguri and Nicolas Kovensky

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Authors (as registered SciPost users):

Sergio Iguri · Nicolas Kovensky

Abstract

We provide a novel local definition for spectrally flowed vertex operators in the SL(2,R)-WZW model, generalising the proposal of Maldacena and Ooguri in [arXiv:hep-th/0111180] 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, and the methods introduced recently by Dei and Eberhardt in [arXiv:2105.12130] based on local Ward identities. We show that the auxiliary variable y used in the latter paper 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 [arXiv:2105.12130] for y-space structure constants of three-point functions with arbitrary spectral flow charges.

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