Integrating out the fermions in AdS

Abstract

Not much is known about superstring scattering amplitudes in curved backgrounds. Using the hybrid formalism in $\rm AdS_3 \times S^3$ with pure NS-NS three-form flux, we compute a $\rm PSU(1,1|2)$-covariant three-point amplitude for half-BPS vertex operators inserted on the $\rm AdS_3$ boundary and show that it agrees with the RNS computation. The zero-mode prescription for the fermions in $\rm AdS$ 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 $\rm AdS$ bulk.