Topological Hypermultiplet on N = 2 Twisted Superspace in Four Dimensions

Abstract

We propose a N =2 twisted superspace formalism with a central charge in four dimensions by introducing a Dirac-Kähler twist. Using this formalism, we construct a twisted hypermultiplet action and find an explicit form of fermionic scalar, vector and tensor transformations. We construct an off-shell Donaldson-Witten theory coupled to the twisted hypermultiplet. We show that this action possesses N =4 twisted supersymmetry at the on-shell level. It turns out that the four-dimensional Dirac-Kähler twist is equivalent to Marcus' twist.

Field representations of vector supersymmetry

“…The scalar and the two-form are even and the vector is odd, or the other way around. We show that this is a truncation of a representation of the topologically twisted N = 2 theory given in [11] (see also [12]). Since in this paper we are mainly interested in representations in Minkowski spacetime, we discuss the existence of a similar multiplet in Minkowskian signature.…”

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

“…We then introduced the bosonic superfields with a scalar and an anti-self-dual tensor indices, V + and V + A respectively, while we introduced the bosonic superfields V µ with a vector index in the previous paper. The theory given by using the superfield with the vector index is as a result Marcus's theory [25]. In the scalar and the tensor superfields case we have derived the off-shell action with the auxiliary fields K + and K + A by imposing the constraints on the superfields from the R-symmetry.…”

“…We pointed out that the hypermultiplet action coupling to the gauge multiplet possess the twisted N=4 supersymmetry at on-shell level [25]. We will investigate the N=4 twisted supersymmetry in this case.…”

“…In a previous paper [25] we derived the N=2 twisted SUSY algebra and superspace formalism with a central charge with respect to the Dirac-Kähler fermion [64,65]. This algebra is a twisted version of the ordinary N=2 SUSY algebra with a central charge [66,67].…”

“…In previous paper [25] we constructed a N=2 twisted superspace formalism with a central charge using the Dirac-Kähler twist. Our formulation was based on a tensor formulation coming from the Dirac-Kähler twisting procedure.…”