N=4 Twisted Superspace from Dirac-Kahler Twist and Off-shell SUSY Invariant Actions in Four Dimensions

TL;DR

This paper develops a four-dimensional N=4 twisted superspace formalism using Dirac-Kahler twist, introduces new supercharges, and constructs off-shell invariant actions, advancing the understanding of twisted supersymmetric theories.

Contribution

It introduces a novel N=4 twisted superspace formalism with Dirac-Kahler twist and constructs off-shell invariant actions, expanding the toolkit for supersymmetric gauge theories.

Findings

Constructed off-shell twisted N=4 SUSY invariant actions.

Identified vector and tensor twisted supercharges.

Decomposed N=4 superalgebra into N=2 sectors.

Abstract

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