Seven-Dimensional Super-Yang-Mills Theory in N=1 Superfields

TL;DR

This paper presents a gauge-covariant formulation of seven-dimensional super-Yang-Mills theory using N=1 superfields, highlighting the unique dimensional cases where such a formulation is possible, with an emphasis on symmetry properties.

Contribution

It introduces a novel gauge-covariant N=1 superfield formulation for 7D super-Yang-Mills theory and analyzes why only 5 and 7 dimensions admit this formulation.

Findings

Formulation expressed in terms of field strengths and a Chern--Simons-like superpotential.

Each term is manifestly N=1 supersymmetric, Lorentz invariant, and gauge invariant.

Only five and seven dimensions support this superfield formulation.

Abstract

We give a gauge-covariant formulation of seven-dimensional super-Yang-Mills theory in terms of N=1 superfields. Furthermore, we show that five and seven dimensions are the only cases where such a formulation exists by analysing the interplay of Lorentz and R symmetries. The action is expressed in terms of field strengths and a Chern--Simons-like superpotential. Each term is manifestly N=1 supersymmetric, Lorentz invariant in four dimensions and gauge invariant under superfield gauge transformations, including those that do not preserve Wess--Zumino gauge.