Vafa-Witten Theory on N=2 and N=4 Twisted Superspace in Four Dimensions

TL;DR

This paper develops a new off-shell twisted hypermultiplet in four-dimensional superspace, constructs a Donaldson-Witten theory coupled to it, and demonstrates the emergence of Vafa-Witten type N=4 twisted supersymmetry.

Contribution

It introduces a novel off-shell twisted hypermultiplet and formulates a Donaldson-Witten theory with N=4 twisted supersymmetry in four dimensions.

Findings

Constructed a new off-shell twisted hypermultiplet.

Formulated a Donaldson-Witten theory coupled to the hypermultiplet.

Demonstrated Vafa-Witten type N=4 twisted supersymmetry at the on-shell level.

Abstract

We construct a new off-shell twisted hypermultiplet with a scalar and an anti-self-dual tensor superfields. Using the N=2 twisted superspace formalism, we construct a Donaldson-Witten theory coupled to the hypermultiplet. We show that this action possesses the Vafa-Witten type N=4 twisted supersymmetry at the on-shell level. We also reconstruct the action using a N=4 twisted superconnection formalism.