The cohomology of superspace, pure spinors and invariant integrals

TL;DR

This paper reviews the superform method for constructing supersymmetric invariants, discusses cohomological techniques, and applies these to higher-order string theory corrections, providing new insights into superspace cohomology.

Contribution

It introduces cohomological methods for analyzing closed superforms and applies them to compute higher-order corrections in heterotic string theory and other supersymmetric models.

Findings

Superform construction effectively generates supersymmetric invariants.

Higher-order heterotic string corrections up to α'^3 are analyzed.

Partial results for N=2, d=10 and N=1, d=11 supersymmetry are presented.

Abstract

The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to $\a'^3$. Some partial results on $N=2,d=10$ and $N=1,d=11$ are also given.