N=2 Harmonic Superforms, Multiplets and Actions

TL;DR

This paper develops a formalism for superforms in N=2 harmonic superspace, analyzing forms up to degree 6 to derive various N=2 actions and exploring the structure of supermultiplets and chains of forms.

Contribution

It introduces a comprehensive analysis of superforms in N=2 harmonic superspace, including higher forms, to systematically derive N=2 action formulas and reveal multiple form chains.

Findings

Reproduces known N=2 action formulas from 4-6 forms.

Identifies multiple chains of superforms in N=2 harmonic superspace.

Provides a foundation for extending to supergravity.

Abstract

In this paper we develop the formalism to study superforms in N=2 harmonic superspace. We perform a thorough (if not complete) analysis of the superforms starting from 0-form and moving all the way up to 6-form. Like the N=1 case we find that the lower superforms (0,1,2,3) describe the various important N=2 supermultiplets. Also, the forms form chains, the field strength of 0-form being related to the gauge form of the 1-form, and so on. However, an important difference with the N=1 case is that there is now more than one chain. Our main aim was to study the higher-forms (4,5,6) to obtain the various N=2 action formulas via the ectoplasmic approach. Indeed, we reproduce the three known action formulas involving a volume integral, a contour integral and no integral over the harmonic subspace from the 6, 5 and 4-form analysis respectively. The next aim is to generalize the analysis to curved space-time (supergravity).