N=2 Super Yang Mills Action and BRST Cohomology

Abstract

The extended BRST cohomology of N=2 super Yang-Mills theory is discussed in the framework of Algebraic Renormalization. In particular, N=2 supersymmetric descent equations are derived from the cohomological analysis of linearized Slavnov-Taylor operator $\B$. It is then shown that both off- and on-shell N=2 super Yang-Mills actions are related to a lower-dimensional gauge invariant field polynomial $Tr\f^2$ by solving these descent equations. Moreover, it is found that these off- and on-shell solutions differ only by a $\B-$exact term, which can be interprated as a consequence of the fact that the cohomology of both cases are the same.