N=4 supersymmetric Eguchi-Hanson sigma model in d=1

TL;DR

This paper constructs a novel N=4 supersymmetric mechanics model with a non-conformally flat target space, specifically focusing on the Eguchi-Hanson space, and explores its properties and construction methods.

Contribution

It introduces a new approach to building N=4 supersymmetric mechanics with non-conformally flat target spaces, exemplified by the Eguchi-Hanson model, and demonstrates the equivalence of different construction methods.

Findings

Successfully constructed the Eguchi-Hanson supersymmetric model.

Established equivalence between standard and quotient approaches.

Provided explicit target space metric expression.

Abstract

We show that it is possible to construct a supersymmetric mechanics with four supercharges possessing not conformally flat target space. A general idea of constructing such models is presented. A particular case with Eguchi--Hanson target space is investigated in details: we present the standard and quotient approaches to get the Eguchi--Hanson model, demonstrate their equivalence, give a full set of nonlinear constraints, study their properties and give an explicit expression for the target space metric.