Pure Spinor Superstrings on Generic type IIA Supergravity Backgrounds

TL;DR

This paper derives the pure spinor superstring sigma model on generic type IIA supergravity backgrounds, establishing a direct link between supergravity fields and the superstring formulation with explicit BRST and kappa-symmetry invariance.

Contribution

It provides a systematic derivation of the pure spinor superstring action on generic type IIA backgrounds using FDA, including explicit BRST transformations and new pure spinor constraints.

Findings

Derived the FDA for type IIA supergravity in string frame.

Constructed the Green-Schwarz and pure spinor sigma models with invariance checks.

Explicit form of BRST transformations and pure spinor constraints provided.

Abstract

We derive the Free Differential Algebra for type IIA supergravity in 10 dimensions in the string frame. We provide all fermionic terms for all curvatures. We derive the Green-Schwarz sigma model for type IIA superstring based on the FDA construction and we check its invariance under kappa-symmetry. Finally, we derive the pure spinor sigma model and we check the BRST invariance. The present derivation has the advantage that the resulting sigma model is constructed in terms of the superfields appearing in the FDA and therefore one can directly relate a supergravity background with the corresponding sigma model. The complete explicit form of the BRST transformations is given and some new pure spinor constraints are obtained. Finally, the explicit form of the action is given.