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

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.

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