Pure Spinor Formalism as an N=2 Topological String

TL;DR

This paper reformulates the pure spinor superstring as an N=2 topological string, enabling new computational techniques and applications in superstring theory and superstring field theory.

Contribution

It introduces a non-minimal set of fields and constructs an N=2 topological string formalism, providing novel methods for superstring amplitude calculations and field theory formulations.

Findings

Multiloop superstring amplitudes computed without picture-changing operators

Construction of a cubic open superstring field theory free of contact-term issues

A four-dimensional pure spinor formalism for F-term computations

Abstract

Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the superstring. Twisted $\hat c$=3 N=2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincare covariant computation of multiloop superstring amplitudes without picture-changing operators, the construction of a cubic open superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action.