General recursion relations for higher-point spectrally flowed correlators

Derive general recursion relations for n-point (n>3) worldsheet correlation functions with spectrally flowed insertions in the SL(2,R) WZW model on AdS3, extending the local Ward-identity approach and formulating the relations in the y-basis as differential equations that can be solved for generic spectral flow data.

Background

Using local Ward identities, the paper derives a system of constraints that become recursion relations among spectrally flowed primary correlators and their h-shifted counterparts. This program is completed for three-point functions (and partially for four-point functions), but a general derivation for higher-point n remains unavailable. Developing these recursions in full generality, ideally cast as y-basis differential equations, would systematically determine flowed higher-point correlators.

References

For higher point functions it is not known how to derive the general expressions of the recursion relations, although important progress was achieved in for n=4.

Lecture notes on strings in AdS$_3$ from the worldsheet and the AdS$_3$/CFT$_2$ duality  (2601.06697 - Kovensky, 10 Jan 2026) in Subsection "The recursion relations"