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On spectrally flowed local vertex operators in AdS$_3$
by Sergio Iguri and Nicolas Kovensky
This Submission thread is now published as
Submission summary
| Submission information |
| Preprint Link: |
scipost_202208_00011v3
(pdf)
|
| Date accepted: |
2022-10-06 |
| Date submitted: |
2022-09-28 11:07 |
| Submitted by: |
Kovensky, Nicolas |
| Submitted to: |
SciPost Physics |
| Ontological classification |
| Academic field: |
Physics |
| Specialties: |
- High-Energy Physics - Theory
|
| Approach: |
Theoretical |
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.
Author comments upon resubmission
Ref.[41] added.
