Flat Symplectic Bundles of N-Extended Supergravities, Central Charges and Black-Hole Entropy

TL;DR

This paper presents a geometric framework for N-extended supergravities using flat symplectic bundles, exploring duality symmetries, central charges, and their relation to black-hole entropy and attractor points.

Contribution

It generalizes N=2 special geometry to N-extended supergravities, linking duality symmetries to flat symplectic bundles and defining central charges as sections over these bundles.

Findings

Relation between duality symmetries and flat symplectic bundles

Definition of central charges as sections over bundles

Analysis of attractor points and black-hole entropy

Abstract

In these lectures we give a geometrical formulation of N-extended supergravities which generalizes N=2 special geometry of N=2 theories. In all these theories duality symmetries are related to the notion of "flat symplectic bundles" and central charges may be defined as "sections" over these bundles. Attractor points giving rise to "fixed scalars" of the horizon geometry and Bekenstein-Hawking entropy formula for extremal black-holes are discussed in some details.