Explaining Pure Spinor Superspace

TL;DR

This paper explains the pure spinor superspace formalism for superstrings and supermembranes, utilizing the superform method to construct supersymmetric invariants in various dimensions and backgrounds.

Contribution

It introduces a clear explanation of pure spinor superspace using the superform method, extending the understanding of supersymmetric invariants in higher dimensions.

Findings

Superform method effectively explains pure spinor superspace.

Construction of supersymmetric invariants in curved supergravity backgrounds.

Generalization of chiral superspace to higher dimensions.

Abstract

In the pure spinor formalism for the superstring and supermembrane, supersymmetric invariants are constructed by integrating over five $\theta$'s in d=10 and over nine $\theta$'s in d=11. This pure spinor superspace is easily explained using the superform (or ''ectoplasm'') method developed by Gates and collaborators, and generalizes the standard chiral superspace in d=4. The ectoplasm method is also useful for constructing d=10 and d=11 supersymmetric invariants in curved supergravity backgrounds.