Abstract
This paper describes a fully covariant approach to harmonic superspace. It is based on the conformal superspace description of conformal supergravity and involves extending the supermanifold M^{4|8} by the tangent bundle of CP^1. The resulting superspace M^{4|8} x TCP^1 can be identified in a certain gauge with the conventional harmonic superspace M^{4|8} x S^2. This approach not only makes the connection to projective superspace transparent, but simplifies calculations in harmonic superspace significantly by eliminating the need to deal directly with supergravity prepotentials. As an application of the covariant approach, we derive from harmonic superspace the full component action for the sigma model of a hyperkahler cone coupled to conformal supergravity. Further applications are also sketched.
Highlights
N = 2 supersymmetric theories in four dimensions face a particular hurdle relative to their N = 1 cousins: the general matter hypermultiplet cannot be off-shell without introducing an infinite number of auxiliary fields
This paper describes a fully covariant approach to harmonic superspace
As an application of the covariant approach, we derive from harmonic superspace the full component action for the sigma model of a hyperkahler cone coupled to conformal supergravity
Summary
This will cover some similar ground as [25, 26], but where these authors were concerned with Einstein supergravity (with two hidden implicit compensators within the supergeometry), we will build conformal supergravity into the structure group of superspace from the very beginning This so-called conformal superspace approach, which corresponds to the superconformal tensor calculus in components, offers significant simplifications to calculations: recent applications have included constructing previously unknown higher-derivative invariants in 5D as well as the construction of all off-shell 3D N ≤ 6 conformal supergravity actions, including auxiliary fields [30, 31].3. A technical appendix addresses aspects of integration on analytic submanifolds, to which we will refer as needed
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