Our article: G. Sardanashvily, W. Wachowski, SUSY gauge theory on graded manifolds, arXiv: 1406.6318
Lagrangian classical field theory of even and odd fields is adequately formulated in terms of fibre bundles and graded manifolds. In particular, conventional Yang-Mills gauge theory is theory of connections on smooth principal bundles, but its BRST extension involves odd ghost fields an antifields on graded manifolds. Here, we formulate Yang-Mills theory of Grassmann-graded gauge fields associated to Lie superalgebras on principal graded bundles. A problem lies in a geometric definition of odd gauge fields. Our goal is Yang--Mills theory of graded gauge fields and its BRST extension.
Conventional Yang–Mills theory of classical gauge fields is adequately formulated as Lagrangian theory of principal connections on smooth principal bundles. Here, we aim to develop Yang–Mills theory of Grassmann-graded even and odd gauge fields associated to Lie superalgebras which characterize various SUSY extensions of Standard Model. A key point is the geometric description of odd gauge fields. A main contradiction is that gauge fields are affine objects, whereas odd fields are linear. A problem also lies in definition of odd fields and their jets.