Pure Spinor Approach to Type IIA Superstring Sigma Models and Free Differential Algebras

TL;DR

This paper develops a pure spinor formalism for type IIA superstring sigma models by extending free differential algebras with BRS symmetry, deriving pure spinor constraints, and obtaining the superstring action in general backgrounds.

Contribution

It introduces a novel formalism combining free differential algebras with BRS symmetry to derive pure spinor constraints and the superstring action in a unified framework.

Findings

Derived BRS transformations for fields and ghosts.

Obtained pure spinor constraints on lambda's.

Reproduced the superstring action in general backgrounds.

Abstract

This paper considers the Free Differential Algebra and rheonomic parametrization of type IIA Supergravity, extended to include the BRS differential and the ghosts. We consider not only the ghosts lambda's of supersymmetry but also the ghosts corresponding to gauge and Lorentz transformations. In this way we can derive not only the BRS transformations of fields and ghosts but also the standard pure spinor constraints on lambda's. Moreover the formalism allows to derive the action for the pure spinor formulation of type IIA superstrings in a general background, recovering the action first obtained by Berkovits and Howe.