Integrating out the fermions in AdS

Not much is known about superstring scattering amplitudes in curved backgrounds. Using the hybrid formalism in $\mathrm{A}\mathrm{d}{\mathrm{S}}_3\times {\mathrm{S}}^3$ with pure NS-NS three-form flux, we compute a $\mathrm{P}\mathrm{S}\mathrm{U}(1,1\mathrm{\mid }2)$-covariant three-point amplitude for half-BPS vertex operators inserted on the $\mathrm{A}\mathrm{d}{\mathrm{S}}_3$ boundary and show that it agrees with the RNS computation. The zero-mode prescription for the fermions in $\mathrm{A}\mathrm{d}\mathrm{S}$ 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 $\mathrm{A}\mathrm{d}\mathrm{S}$ bulk.