Integrating out the fermions in AdS

Abstract

Not much is known about superstring scattering amplitudes in curved backgrounds. Using the hybrid formalism in AdS3 × S3 with pure NS-NS three-form flux, we compute a PSU(1, 1|2)-covariant three-point amplitude for half-BPS vertex operators inserted on the AdS3 boundary and show that it agrees with the RNS computation. The zero-mode prescription for the fermions in AdS is defined in terms of the “standard” spacetime SUSY generator. It is found that integrating out the fermionic worldsheet fields in the path integral gives rise to the target-space vielbein, which explicitly encodes that the conformal group on the boundary is identified with the symmetry group of the AdS bulk.