Projective multiplets and hyperkahler cones in conformal supergravity

TL;DR

This paper reviews how projective superspace facilitates the construction of off-shell actions for hypermultiplets coupled to conformal supergravity, and details the transition to on-shell sigma models with hyperkahler cone target spaces.

Contribution

It provides a comprehensive framework for deriving on-shell N=2 supersymmetric sigma models from superspace formulations, clarifying the geometric data's superspace origin.

Findings

Explicit construction of on-shell hypermultiplet actions in curved superspace

Demonstration of how to eliminate auxiliary fields to obtain physical models

Clarification of the superspace origin of hyperkahler geometric data

Abstract

Projective superspace provides a natural framework for the construction of actions coupling hypermultiplets to conformal supergravity. We review how the off-shell actions are formulated in superspace and then discuss how to eliminate the infinite number of auxiliary fields to produce an on-shell N=2 supersymmetric sigma model, with the target space corresponding to a generic 4n-dimensional hyperkahler cone. We show how the component action coupling the hypermultiplets to conformal supergravity may be constructed starting from curved superspace. The superspace origin of the geometric data -- the hyperkahler potential, complex structures, and any gauged isometries -- is also addressed.