N=1 SYM Action and BRST Cohomology

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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, in the framework of Algebraic Renormalization. Furthermore we show that off and on shell solutions differ only by a - exact term, which is a consequence of the fact that the cohomology of both cases are same.