Abstract
We propose a closed-form formula for genus 0 four-point functions in AdS3 string theory with pure NS-NS flux including arbitrary amounts of spectral flow. Our formula passes many non-trivial consistency checks and has intriguing connections to Hurwitz theory. This paper is the second in a series with several instalments.
Highlights
The duality between strings propagating on three-dimensional Anti-de Sitter space (AdS3) and two-dimensional conformal field theories (CFT2) is one of the best understood incarnations of the AdS/CFT correspondence [1]
A complete understanding of the spectrum of the SL(2, R) WZW model has not been reached until the need to introduce spectral flow was realised [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]
While the spectrum of the worldsheet theory is under a firm control, the presence of spectral flow has hampered a full understanding of AdS3 string correlators
Summary
The duality between strings propagating on three-dimensional Anti-de Sitter space (AdS3) and two-dimensional conformal field theories (CFT2) is one of the best understood incarnations of the AdS/CFT correspondence [1]. One can see that there is another integer associated to each vertex operator — the so-called spectral flow w ∈ Z≥0 It corresponds to the number of times the worldsheet is winding around the insertion point in the boundary.. For genus 0 four-point functions, we propose a map that takes an unflowed correlation function and transforms it into a flowed correlation function with the desired spectral flow indices Notice that this is not just a rewriting of the problem, since in the unflowed sector (i.e. the case where all vertex operators satisfy wi = 0) these correlators are very well-known and have been thoroughly studied in the literature, see e.g. Various appendices complement the discussion of some technical points we encounter throughout the text
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