Topological hypermultiplet on N=2 twisted superspace in four dimensions

TL;DR

This paper develops a four-dimensional N=2 twisted superspace formalism incorporating a Dirac-Kähler twist, constructs a hypermultiplet action, and demonstrates its relation to N=4 twisted supersymmetry and Marcus's twist.

Contribution

It introduces a novel N=2 twisted superspace formalism with a Dirac-Kähler twist and constructs a corresponding hypermultiplet action with explicit supersymmetry transformations.

Findings

Constructed a twisted hypermultiplet action in four dimensions.

Showed the equivalence of Dirac-Kähler twist to Marcus's twist.

Demonstrated N=4 twisted supersymmetry at on-shell level.

Abstract

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