Untwisting the Pure Spinor Formalism to the RNS and Twistor String in a Flat and $AdS_5\times S^5$ Background

TL;DR

This paper reformulates the pure spinor superstring formalism as an N=1 worldsheet theory, unifies it with RNS and twistor strings, and extends it to curved backgrounds like AdS_5×S^5, simplifying the description and potentially aiding amplitude calculations.

Contribution

It introduces an N=1 worldsheet superfield framework unifying pure spinor, RNS, and twistor formalisms, and constructs a simple, manifestly symmetric AdS_5×S^5 superstring action.

Findings

Unified pure spinor, RNS, and twistor formalisms via N=1 superfields.

Derived a simple AdS_5×S^5 superstring action with PSU(2,2|4) symmetry.

Extended the formalism to curved backgrounds with manifest supersymmetry.

Abstract

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 $\Theta^\alpha$ together with a superfield constraint relating $DX^m$ and $D\Theta^\alpha$. The constraint implies that the worldsheet superpartner of $\theta^\alpha$ 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 $AdS_5\times S^5$ background in terms of the twistor superfields. This $AdS_5\times S^5$ worldsheet action is a remarkably simple fermionic coset model with manifest $PSU(2,2|4)$ symmetry and might be useful for computing $AdS_5\times S^5$ superstring scattering amplitudes.