SUSY gauge theory on graded manifolds

Abstract

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.