D=10 Super-Yang-Mills at O(alpha'^2)

TL;DR

This paper constructs the complete D=10 super-Yang-Mills action at the alpha'^2 level using superspace techniques, detailing Lorentz structures and supersymmetry constraints without approximations.

Contribution

It provides the most general form of the D=10 super-Yang-Mills action at order alpha'^2, including Lorentz and gauge group structures, and analyzes supersymmetry constraints.

Findings

Complete alpha'^2 corrections determined

Lorentz structure fully specified

Supersymmetry constraints partially restrict gauge structure

Abstract

Using superspace techniques, the complete and most general action of D=10 super-Yang--Mills theory is constructed at the alpha'^2 level. No other approximations, e.g., keeping only a subset of the allowed derivative terms, are used. The Lorentz structure of the alpha'^2 corrections is completely determined, while (depending on the gauge group) there is some freedom in the adjoint structure, which is given by a totally symmetric four-index tensor. We examine the second, non-linearly realised supersymmetry that may be present when the gauge group has a U(1) factor, and find that the constraints from linear and non-linear supersymmetry to a large extent coincide. However, the additional restrictions on the adjoint structure of the order alpha'^2 interactions following from the requirement of non-linear supersymmetry do not completely specify the symmetrised trace prescription.