Semichiral Sigma Models with 4D Hyperkaehler Geometry

TL;DR

This paper investigates semichiral sigma models with four-dimensional target spaces, revealing that extended on-shell supersymmetry leads to hyperkähler geometry and providing explicit examples.

Contribution

It analyzes the extended on-shell supersymmetry of semichiral sigma models, showing that a general ansatz results in hyperkähler geometry without involving central charge transformations.

Findings

Extended on-shell supersymmetry implies hyperkähler geometry.

Provided explicit examples of such models.

Clarified the structure of non-manifest supersymmetries.

Abstract

Semichiral sigma models with a four-dimensional target space do not support extended N=(4,4) supersymmetries off-shell arXiv:0903.2376, arXiv:0912.4724. We contribute towards the understanding of the non-manifest on-shell transformations in (2,2) superspace by analyzing the extended on-shell supersymmetry of such models and find that a rather general ansatz for the additional supersymmetry (not involving central charge transformations) leads to hyperk\"ahler geometry. We give non-trivial examples of these models.