Free Differential Algebras and Pure Spinor Action in IIB Superstring Sigma Models

TL;DR

This paper extends the pure spinor formalism to IIB superstring sigma models by deriving BRST transformations and pure spinor constraints from free differential algebras, and constructs the pure spinor action in curved backgrounds.

Contribution

It introduces a method to derive the pure spinor action for IIB superstrings from supergravity algebra, matching previous results by Berkovits and Howe.

Findings

Derived BRST transformations and pure spinor constraints for IIB superstrings.

Constructed the pure spinor action in curved supergravity backgrounds.

Validated the approach by agreement with known actions.

Abstract

In this paper we extend to the case of IIB superstring sigma models the method proposed in hep-th/10023500 to derive the pure spinor approach for type IIA sigma models. In particular, starting from the (Free) Differential Algebra and superspace parametrization of type IIB supergravity, extended to include the BRST differential and all the ghosts, we derive the BRST transformations of fields and ghosts as well as the standard pure spinor constraints for the ghosts $\lambda $ related to supersymmetry. Moreover, using the method first proposed by us, we derive the pure spinor action for type IIB superstrings in curved supergravity backgrounds (on shell), in full agreement with the action first obtained by Berkovits and Howe.