U-Duality and Central Charges in Various Dimensions Revisited

TL;DR

This paper presents a geometric framework for extended supergravities across various dimensions, highlighting duality symmetries, central charges, and symplectic structures, especially in four-dimensional N-extended theories.

Contribution

It introduces a unified geometric formulation that makes duality symmetries explicit and generalizes special geometry for N>2 supergravities.

Findings

Manifest duality symmetries in supergravity theories

Construction of central and matter charges in various dimensions

Identification of a flat symplectic bundle for N>2 theories

Abstract

A geometric formulation which describes extended supergravities in any dimension in presence of electric and magnetic sources is presented. In this framework the underlying duality symmetries of the theories are manifest. Particular emphasis is given to the construction of central and matter charges and to the symplectic structure of all D=4, N-extended theories. The latter may be traced back to the existence, for N>2, of a flat symplectic bundle which is the N>2 generalization of N=2 Special Geometry.