Formula omitted] twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

Abstract

We propose a N = 4 twisted superspace formalism in four dimensions by introducing a Dirac–Kähler twist. In addition to the BRST charge as a scalar counter part of the twisted supercharge we find vector and tensor twisted supercharges. By introducing twisted chiral superfields we explicitly construct an off-shell twisted N = 4 SUSY invariant action. We propose a variety of supergauge invariant actions by introducing twisted vector superfields. We may, however, need to find further constraints in order to identify a twisted N = 4 super-Yang–Mills action. We propose a superconnection formalism for the twisted superspace and constraints play a crucial role in the construction. It turns out that the N = 4 superalgebras obtained by a Dirac–Kähler twist can be decomposed into N = 2 sectors. We then construct twisted N = 2 super-Yang–Mills actions using this formalism in two and four dimensions.