Spinorial cohomology of abelian d=10 super-Yang-Mills at alpha'^3

TL;DR

This paper demonstrates that at order alpha'^3, the spinorial cohomology of ten-dimensional abelian super-Yang-Mills theory is trivial, implying no supersymmetric corrections at this order and supporting the uniqueness of such deformations.

Contribution

It provides a computation of spinorial cohomology at alpha'^3 and shows its triviality, indicating no supersymmetric deformations at this order in abelian d=10 SYM.

Findings

Spinorial cohomology at alpha'^3 is trivial.

Linear supersymmetry excludes alpha'^3 corrections.

Supports the conjecture of a unique supersymmetric deformation.

Abstract

We compute the spinorial cohomology of ten-dimensional abelian SYM at order alpha'^3 and we find that it is trivial. Consequently, linear supersymmetry alone excludes the presence of alpha'^3-order corrections. Our result lends support to the conjecture that there may be a unique supersymmetric deformation of ordinary ten-dimensional abelian SYM.