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

The pure spinor formalism for the superstring can be formulated as a twisted n=2 worldsheet theory with fermionic generators j brst and composite b ghost. after untwisting the formalism to an n=1 worldsheet theory with fermionic stress tensor j brst + b, the worldsheet variables combine into n=1 worldsheet superfields x m and θ α together with a superfield constraint relating dx m and dθ α . the constraint implies that the worldsheet superpartner of θ α 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 × s 5 background in terms of the twistor superfields. this ads5 × s 5 worldsheet action is a remarkably simple fermionic coset model with manifest psu(2, 2|4) symmetry and might be useful for computing ads5 × s 5 superstring scattering amplitudes.