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 ϕ2 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.