The Symplectic Structure of N=2 Supergravity and its Central Extension

TL;DR

This paper explores the symplectic structure of N=2 supergravity in four dimensions, detailing how electric and magnetic charges relate to special geometry, with applications to Type IIB string compactifications on Calabi-Yau manifolds.

Contribution

It provides a general formulation of electric and magnetic charges in N=2 supergravity, emphasizing the symplectic structure and its application to string theory compactifications.

Findings

Derived formulae for moduli-dependent electric and magnetic charges.

Highlighted the symplectic structure underlying special geometry.

Applied the framework to Type IIB string compactifications on Calabi-Yau manifolds.

Abstract

We report on the formulation of $N=2$ $D=4$ supergravity coupled to $n_V$ abelian vector multiplets in presence of electric and magnetic charges. General formulae for the (moduli dependent) electric and magnetic charges for the $n_V+1$ gauge fields are given which reflect the symplectic structure of the underlying special geometry. The specification to Type IIB strings compactified on Calabi-Yau manifolds, with gauge group $U(1)^{h_{21}+1}$ is given.