Central Extension of Extended Supergravities in Diverse Dimensions

TL;DR

The paper extends central-charge identities from $N=2$ Special Geometry to $N$-extended supergravities in dimensions $4 \le D < 10$, for $p$-extended objects, by expressing charges as dressed field strengths tied to the duality coset $G/H$. It derives differential relations and sum rules for central and matter charges from the coset geometry and applies Gaillard–Zumino dualities and symplectic embeddings to describe dyons in $D=4$. The authors analyze extremization of the ADM mass per unit $p$-volume for BPS states and reveal group-theoretical conditions under which extremal branes have finite horizon entropy, showing absence of finite-entropy extremal $0$-branes for $D>5$ in theories with 16 or more supercharges and identifying lower-dimensional exceptions. The work provides a unified geometric framework to study BPS spectra, moduli dependence, and phase transitions across diverse supergravity theories relevant to string/M-theory compactifications.

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.