Untwisting the pure spinor formalism to the RNS and twistor string in a flat and AdS5 × S 5 background

Abstract

Abstract: The pure spinor formalism for the superstring can be formulated as a twisted N=2 worldsheet theory with fermionic generators jBRST and composite b ghost. After untwisting the formalism to an N=1 worldsheet theory with fermionic stress tensor jBRST + b, the worldsheet variables combine into N=1 worldsheet superfields Xm and Θα together with a superfield constraint relating DXm and DΘα. The constraint implies that the worldsheet superpartner of θα is a bosonic twistor variable, and different solutions of the constraint give rise to the pure spinor or extended RNS formalisms, as well as a new twistor-string formalism with manifest N=1 worldsheet supersymmetry. These N=1 worldsheet methods generalize in curved Ramond-Ramond backgrounds, and a manifestly N=1 worldsheet supersymmetric action is proposed for the superstring in an AdS5 × S5 background in terms of the twistor superfields. This AdS5 × S5 worldsheet action is a remarkably simple fermionic coset model with manifest PSU(2, 2|4) symmetry and might be useful for computing AdS5 × S5 superstring scattering amplitudes.