Special Kahler Manifolds

TL;DR

This paper provides an intrinsic definition of special Kahler geometry in the context of N=2 supersymmetry, linking it to integrable systems and hyperkahler metrics, and extends the concept to supergravity.

Contribution

It introduces an intrinsic definition of special Kahler manifolds and relates them to algebraic integrable systems and hyperkahler geometry, extending the framework to supergravity.

Findings

Special Kahler manifolds are intrinsically defined in global N=2 supersymmetry.

These manifolds are related to algebraic integrable systems under an integrality hypothesis.

The cotangent bundle of a special Kahler manifold admits a hyperkahler metric.

Abstract

We give an intrinsic definition of the special geometry which arises in global N=2 supersymmetry in four dimensions. The base of an algebraic integrable system exhibits this geometry, and with an integrality hypothesis any special Kahler manifold is so related to an integrable system. The cotangent bundle of a special Kahler manifold carries a hyperkahler metric. We also define special geometry in supergravity in terms of the special geometry in global supersymmetry.