On compactified harmonic/projective superspace, 5D superconformal theories, and all that

TL;DR

This paper explores the superconformal structure of 4D N=2 and 5D superspaces using supertwistor methods, deriving transformation laws, supermultiplets, and actions, including theories with gauged central charge.

Contribution

It introduces a detailed analysis of superconformal structures in 4D and 5D superspaces, including new supermultiplets and superconformal actions in harmonic and projective formalisms.

Findings

Derived superconformal Killing vectors for 5D theories

Presented off-shell superconformal multiplets in harmonic and projective superspaces

Constructed examples of 5D superconformal theories with gauged central charge

Abstract

Within the supertwistor approach, we analyse the superconformal structure of 4D N = 2 compactified harmonic/projective superspace. In the case of 5D superconformal symmetry, we derive the superconformal Killing vectors and related building blocks which emerge in the transformation laws of primary superfields. Various off-shell superconformal multiplets are presented both in 5D harmonic and projective superspaces, including the so-called tropical (vector) multiplet and polar (hyper)multiplet. Families of superconformal actions are described both in the 5D harmonic and projective superspace settings. We also present examples of 5D superconformal theories with gauged central charge.