Acknowledgements: We thank Andrea Dei, Yasuaki Hikida, Matthias Gaberdiel, Sylvain Lacriox, Nathan McStay, Kiarash Naderi, Beat Nairz, Ron Reid-Edwards, Volker Schomerus, and David Skinner for useful discussions. We also thank Andrea Dei, Lorenz Eberhardt, Matthias Gaberdiel, Ron Reid-Edwards and David Skinner for useful comments on an early version of the draft. We further thank Yasuaki Hikida and Volker Schomerus for sharing a preliminary version of their recent paper [32]. The work of VS is supported by a grant from the Swiss National Science Foundation. VS also acknowledges the support by the NCCR SwissMAP that is also supported by the Swiss National Science Foundation. The work of BK and SS is supported by STFC consolidated grants ST/T000694/1 and ST/X000664/1. The work of SS is also supported by the Trinity Internal Graduate studentship.Abstract
We study string theory in three-dimensional Anti-de Sitter spacetime in the path integral formalism. We derive expressions for generic spectrally-flowed near-boundary vertex operators in the Wakimoto representation, and relate their correlation functions to covering maps from the worldsheet to the target space boundary. We show that the path integral structurally reproduces correlation functions of the dual symmetric orbifold theory. By rephrasing spectral flow as the introduction of a background gauge field, we provide a path integral derivation of the localisation property of the near boundary theory. We then focus on the case of IIB string theory on AdS3 × S3 × 4 with k = 1 units of NS-NS flux, where the relationship between correlation functions and covering maps can be made sharp. We also comment on the relation of the k = 1 theory and twistor theory.</jats:p
