N=2 super-Yang-Mills action and BRST cohomology

The extended BRST cohomology of N = 2 super-Yang-Mills theory is discussed in the framework of Algebraic Re normalization. In particular, N = 2 supersymmetric descent I 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 I related to a lower-dimensional gauge-invariant field polynomial Tr phi(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 interpreted as a consequence of the fact that the cohomology of both cases are the same.