N=4 twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

Abstract

We propose N = 4 twisted superspace formalism in four dimensions by introducing Dirac-Kähler 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-Kähler 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.

Topological Hypermultiplet on N = 2 Twisted Superspace in Four Dimensions

“…It should be noted that the Dirac-Kähler twist can be defined in other dimensions [37,58]. The advantage of the Dirac-Kähler twist is that since all the fermions are related to spinor by the Dirac-Kähler mechanism, we can easily construct a corresponding untwisted theory.…”

“…We have investigated the properties of the four dimensional N=4 and N=2 twisted superspace formalism without a central charge in a previous paper [37]. In the N=2 case the Donaldson-Witten theory was constructed in our superspace formulation.…”

Vafa-Witten theory onN= 2 andN= 4 twisted superspace in four dimensions

“…The Dirac-Kähler mechanism gives the way to identify the N = 4 extended SUSY suffix {i} as the Lorentz spinor suffix {α}, i.e. , diagonal subgroup SO(4) ⊗ SO(4) I [21]. The N=4 fermions based on the Dirac-Kähler mechanism consist of two scalar, two vector, a self-dual tensor and an anti-self-dual tensor.…”

An alternative lattice field theory formulation inspired by lattice supersymmetry

“…The relation between these two formulations was made clear in [36][37][38][39]. It has been explicitly shown in the link approach that Q-exact lattice SUSY formulation is essentially the lattice version of continuum twisted super Yang-Mills formulation via Dirac-Kähler twisting procedure [40][41][42]. Although the lattice SUSY formulation of the link approach was based on the local formulation, noncommutativity is needed for the Hopf algebraic consistency.…”