Supersymmetric Yang-Mills theory at order alpha'^3

TL;DR

This paper constructs the order alpha'^3 supersymmetric Yang-Mills action in ten dimensions for any gauge group, revealing new invariants at odd orders of alpha' and emphasizing their independence from lower-order terms.

Contribution

It provides the explicit form of the alpha'^3 invariant in ten-dimensional supersymmetric Yang-Mills theory for arbitrary gauge groups, highlighting the structure and independence of higher-order invariants.

Findings

Derived the alpha'^3 invariant expressed via structure constants

Showed independence of alpha'^3 from alpha'^2 invariant

Predicted the occurrence of invariants at all odd orders of alpha'

Abstract

We construct the order alpha'^3 terms in the supersymmetric Yang-Mills action in ten dimensions for an arbitrary gauge group. The result can be expressed in terms of the structure constants of the Yang-Mills group, and is therefore independent of abelian factors. The alpha'^3 invariant obtained here is independent of the alpha'^2 invariant, and we argue that additional superinvariants will occur at all odd orders of alpha'.