N=1 SYM Action and BRST Cohomology

TL;DR

This paper explores the connection between BRST cohomology and N=1 supersymmetric Yang-Mills actions in four dimensions, revealing their relation through descent equations and cohomological analysis.

Contribution

It demonstrates that both off-shell and on-shell N=1 SYM actions are related to a lower-dimensional polynomial via descent equations, and shows their cohomological equivalence.

Findings

Off-shell and on-shell actions differ by a B-exact term.

Both actions are connected to a lower-dimensional polynomial.

Cohomology of off-shell and on-shell cases is identical.

Abstract

The relation between BRST cohomology and the N=1 supersymmetric Yang-Mills action in 4 dimensions is discussed. In particular, it is shown that both off and on shell N=1 SYM actions are related to a lower dimensional field polynomial by solving the descent equations, which is obtained from the cohomological analysis of linearized Slavnov-Taylor operator $\B$, in the framework of Algebraic Renormalization. Furthermore we show that off and on shell solutions differ only by a $\B$- exact term, which is a consequence of the fact that the cohomology of both cases are same.