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Integrating out the fermions in AdS
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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.
Forward citations
Cited by 2 Pith papers
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Vertex operators for the superstring with manifest $d=6$ $\mathcal{N}=1$ supersymmetry
A manifestly d=6 N=1 supersymmetric vertex operator and amplitude prescription are constructed for the superstring, with BRST invariance implying the SYM equations of motion.
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Covariant quantization of the superstring in $\rm AdS_3 \times S^3 \times T^4$ with mixed flux
A manifestly supersymmetric and quantizable worldsheet action for the mixed-flux AdS3 x S3 x T4 superstring is constructed and shown to be one-loop conformal.
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