Central Extension of Extended Supergravities in Diverse Dimensions

TL;DR

This paper extends the mathematical framework of N=2 Special Geometry to N-extended supergravity across multiple dimensions, analyzing BPS states and their extremal properties, including entropy considerations.

Contribution

It generalizes central-charge relations and differential identities to N-extended supergravity in various dimensions, providing new insights into BPS states and their extremization.

Findings

Derived generalized central-charge relations for extended supergravities.

Analyzed extremization of ADM mass for BPS extended objects.

Identified conditions leading to vanishing Bekenstein-Hawking entropy.

Abstract

We generalize central-charge relations and differential identities of N=2 Special Geometry to N extended supergravity in any dimension 4 \leq D <10, and p-extended objects. We study the extremization of the ADM mass per unit of p-volume of BPS extended objects. Runaway solutions for a ``dilaton'' degree of freedom leading to a vanishing result are interpreted as BPS extremal states having vanishing Bekenstein-Hawking Entropy.