Five-dimensional non-Abelian supersymmetric Chern-Simons action in projective superspace

In this paper, we derive five-dimensional non-Abelian <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">N</a:mi><a:mo>=</a:mo><a:mn>1</a:mn></a:math> Chern-Simons action from its proposed definition of variation with respect to an infinitesimal deformation of the vector prepotential in a projective superspace setting. It has been a long-standing open problem how to integrate this variation. Now, thanks to the simplicity of a projective superspace technique, we are finally able to obtain this term. Our final result is expressed in terms of the real prepotential multiplets and projective covariant derivatives. The action reduces to the correct formula in the Abelian limit. As a bonus, we also give the supersymmetric Yang-Mills action with a half measure.