Hyper-Kahler geometries and nonlinear supermultiplets

TL;DR

This paper introduces a novel method for constructing supersymmetric sigma-models with hyper-Kahler target spaces by treating the coupling constant as a dynamical variable, enabling models with specific isometries.

Contribution

It presents a new approach to build N=4 and N=8 supersymmetric four-dimensional sigma-models with hyper-Kahler geometries and one isometry, expanding the class of known models.

Findings

Constructed sigma-models with hyper-Kahler target spaces

Achieved models with one isometry commuting with supersymmetry

Demonstrated the method's applicability to N=4 and N=8 cases

Abstract

It is presented a method of construction of sigma-models with target space geometries different from conformally flat ones. The method is based on a treating of a constancy of a coupling constant as a dynamical constraint following as an equation of motion. In this way we build N=4 and N=8 supersymmetric four-dimensional sigma-models in d=1 with hyper-Kahler target space possessing one isometry, which commutes with supersymmetry.