Wess-Zumino and Super Yang-Mills Theories in D=4 Integral Superspace

TL;DR

This paper reconstructs N=1 and N=2 super-Yang-Mills and Wess-Zumino theories in four-dimensional superspace using integral forms, demonstrating their equivalence and discussing the supergeometry involved.

Contribution

It introduces a geometric formalism using integral top forms on supermanifolds to construct and relate supersymmetric theories in four dimensions.

Findings

Demonstrates equivalence of rheonomic and superspace actions.

Provides detailed discussion of supergeometry and integration theory.

Establishes an efficient geometric framework for supersymmetric models.

Abstract

We reconstruct the action of $N=1, D=4$ Wess-Zumino and $N=1, 2, D=4$ super-Yang-Mills theories, using integral top forms on the supermanifold ${\cal M}^{(4|4)}$. Choosing different Picture Changing Operators, we show the equivalence of their rheonomic and superspace actions. The corresponding supergeometry and integration theory are discussed in detail. This formalism is an efficient tool for building supersymmetric models in a geometrical framework.