Superstring four-point functions in AdS$_3\times S^3\times T^4$

Abstract: We study spacetime four-point functions of chiral primary operators for superstrings propagating in AdS$_3\times S^3\times T^4$ from the worldsheet perspective, allowing for external states with arbitrary spectral flow charges. We work at small boundary cross-ratio and consider both extremal (supersymmetry-protected) and non-extremal configurations. The string correlators involve a non-trivial integration over the worldsheet moduli, and we demonstrate how the exchange of short and long strings is encoded in distinct integration regions. We interpret our results in terms of the operator product expansion in the boundary theory, and make explicit the precise matching with the available data for the relevant holographic correlators.