HyperKhaler Metrics Building and Integrable Models

TL;DR

This paper applies integrable system methods to construct and analyze hyperKähler metrics within supersymmetric harmonic superspace, revealing integrability properties and explicit solutions for certain constraint equations.

Contribution

It demonstrates the integrability of specific hyperKähler metric building equations and provides explicit solutions and conserved currents within the supersymmetric framework.

Findings

The constraint equation is shown to be integrable.

Explicit solutions to the equations are constructed.

Conserved currents related to the symmetry are identified.

Abstract

Methods developed for the analysis of integrable systems are used to study the problem of hyperK\"ahler metrics building as formulated in D=2 N=4 supersymmetric harmonic superspace. We show, in particular, that the constraint equation $\beta\partial^{++2}\omega -\xi^{++2}\exp 2\beta\omega =0$ and its Toda like generalizations are integrable. Explicit solutions together with the conserved currents generating the symmetry responsible of the integrability of these equations are given. Other features are also discussed