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

TL;DR

The paper develops a comprehensive framework for 5D superconformal theories by combining harmonic and projective superspace formalisms, anchored in a supertwistor-based view of compactified Minkowski space. It derives 5D superconformal Killing vectors, constructs primary and analytic multiplets, and builds off-shell actions including Chern-Simons and vector-tensor systems, both in harmonic and projective settings. A central theme is realizing 5D ${\cal N}=1$ (eight supercharges) theories with conformal symmetry, including models with gauged central charge and their connections to 4D ${\cal N}=2$ reductions and brane-world/AdS/CFT contexts. The results supply concrete, gauge-invariant, off-shell multiplets and actions that can serve as building blocks for superconformal tensor calculus and 5D supergravity-matter systems. The work thus provides a versatile toolkit for systematic construction of 5D superconformal theories with potential applications in higher-dimensional holography and brane-world physics.

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.