Supersymmetric sigma-models, twistors, and the Atiyah-Hitchin metric

TL;DR

This paper explores the use of Legendre transform techniques in supersymmetric sigma-models to construct hyperkahler metrics, providing a twistor space interpretation and illustrating with the Atiyah-Hitchin metric example.

Contribution

It introduces a twistor space perspective on Legendre transform generalizations for hyperkahler metric construction, exemplified by the Atiyah-Hitchin metric.

Findings

Provides a twistor space interpretation of Legendre transform methods

Demonstrates the approach with the Atiyah-Hitchin metric example

Enhances understanding of hyperkahler metric constructions in supersymmetric theories

Abstract

The Legendre transform and its generalizations, originally found in supersymmetric sigma-models, are techniques that can be used to give constructions of hyperkahler metrics. We give a twistor space interpretation to the generalizations of the Legendre transform construction. The Atiyah-Hitchin metric on the moduli space of two monopoles is used as a detailed example.