Untwisting the Pure Spinor Formalism to the RNS and Twistor String in a Flat and $Ad{S}_5\times S^5$ Background

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 $D{X}^m$ 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 $Ad{S}_5\times S^5$ background in terms of the twistor superfields. This $Ad{S}_5\times S^5$ worldsheet action is a remarkably simple fermionic coset model with manifest $PSU(2,2|4)$ symmetry and might be useful for computing $Ad{S}_5\times S^5$ superstring scattering amplitudes.

30 pages. Corrected typos, added 2 footnotes, and dedicated paper to Mario Tonin

References in corpus (6)

• Ambitwistor strings and the scattering equations
• Infinite Tension Limit of the Pure Spinor Superstring
• Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism
• Simpler Superstring Scattering
• Supersymmetry Breaking Effects using the Pure Spinor Formalism of the Superstring
• Pure Spinor b-ghost in a Super-Maxwell Background

Cited by in corpus (12)

• Tree-level amplitudes from the pure spinor superstring
• Algorithmic construction of SYM multiparticle superfields in the BCJ gauge
• Fermionic one-loop amplitudes of the RNS superstring
• B-RNS-GSS heterotic string in curved backgrounds
• Towards the underlying gauge theory of the pure spinor superstring
• Two-Point Superstring Tree Amplitudes Using the Pure Spinor Formalism
• Closed string disk amplitudes in the pure spinor formalism
• Pure spinor formulation of the superstring and its applications
• Two-loop superstring five-point amplitudes I: Construction via chiral splitting and pure spinors
• D=5 Holomorphic Chern-Simons and the Pure Spinor Superstring
• Quantization of the particle with a linear massless solution
• Tension between string amplitude prescriptions with presumed spacetime supersymmetry