On superconformal projective hypermultiplets

TL;DR

This paper develops a unified framework for four-dimensional N=2 superconformal multiplets in projective superspace, introduces superconformal polar multiplets, and constructs new sigma-models with complex auxiliary field elimination techniques.

Contribution

It provides the first consistent definition of superconformal polar multiplets and presents new superconformal sigma-models using projective superspace techniques.

Findings

Defined superconformal polar multiplets for the first time

Constructed new 4D N=2 superconformal sigma-models

Showed auxiliary fields can be eliminated using supersymmetry considerations

Abstract

Building on the five-dimensional constructions in hep-th/0601177, we provide a unified description of four-dimensional N = 2 superconformal off-shell multiplets in projective superspace, including a realization in terms of N = 1 superfields. In particular, superconformal polar multiplets are consistently defined for the first time. We present new 4D N = 2 superconformal sigma-models described by polar multiplets. Such sigma-models realize general superconformal couplings in projective superspace, but involve an infinite tale of auxiliary N = 1 superfields. The auxiliaries should be eliminated by solving infinitely many algebraic nonlinear equations, and this is a nontrivial technical problem. We argue that the latter can be avoided by making use of supersymmetry considerations. All information about the resulting superconformal model (and hence the associated superconformal cone) is encoded in the so-called canonical coordinate system for a Kaehler metric, which was introduced by Bochner and Calabi in the late 1940s.