Special Kaehler geometry

TL;DR

This paper discusses special Kaehler geometry, a mathematical structure arising from the scalar couplings in N=2 supergravity theories, highlighting its symplectic duality and connections to other geometries.

Contribution

It clarifies the symplectic structure of special Kaehler geometry and relates it to conformal symmetry, quaternionic geometry, and Sasakian manifolds.

Findings

Provides equivalent definitions involving symplectic duality

Connects special Kaehler geometry to quaternionic and Sasakian geometries

Highlights the role of conformal symmetry in the construction

Abstract

The geometry that is defined by the scalars in couplings of Einstein-Maxwell theories in N=2 supergravity in 4 dimensions is denoted as special Kaehler geometry. There are several equivalent definitions, the most elegant ones involve the symplectic duality group. The original construction used conformal symmetry, which immediately clarifies the symplectic structure and provides a way to make connections to quaternionic geometry and Sasakian manifolds.