6D Supersymmetric Nonlinear Sigma-Models in 4D, N=1 Superspace

TL;DR

This paper explores 6D supersymmetric nonlinear sigma-models within 4D, N=1 superspace, presenting two approaches—one using chiral superfields and another related to projective superspace—to describe hypermultiplets.

Contribution

It introduces two distinct superfield formulations for 6D hypermultiplets in 4D, enhancing understanding of supersymmetric sigma-models and their representations.

Findings

Doublet of chiral superfields provides a transparent description.

A second approach relates to projective superspace with different superfield requirements.

Models outside projective superspace are also analyzed.

Abstract

Using 4D, N=1 superfield techniques, a discussion of the 6D sigma-model possessing simple supersymmetry is given. Two such approaches are described. Foremost it is shown that the simplest and most transparent description arises by use of a doublet of chiral scalar superfields for each 6D hypermultiplet. A second description that is most directly related to projective superspace is also presented. The latter necessarily implies the use of one chiral superfield and one nonminimal scalar superfield for each 6D hypermultiplet. A separate study of models of this class, outside the context of projective superspace, is also undertaken.