SUSY gauge theory on graded manifolds

TL;DR

This paper develops a geometric formulation of Yang-Mills gauge theory involving graded manifolds and superalgebras, extending classical gauge theories to include odd fields and their BRST symmetry.

Contribution

It introduces a geometric framework for Yang-Mills theory with Grassmann-graded gauge fields on principal graded bundles, addressing the definition of odd gauge fields.

Findings

Formulation of Yang-Mills theory on graded manifolds.

Extension of BRST symmetry to graded gauge fields.

Clarification of geometric structures for odd gauge fields.

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.