The Complete Form of N=2 Supergravity and its Place in the General Framework of D=4 N--Extended Supergravities

TL;DR

This paper presents a comprehensive, explicit component form of N=2 supergravity in four dimensions with arbitrary couplings, based on advanced geometrical frameworks, facilitating further research in supersymmetry breaking and black hole solutions.

Contribution

It provides the first fully explicit, general component Lagrangian for N=2 supergravity with arbitrary couplings, expanding the toolkit for theoretical investigations.

Findings

Explicit component Lagrangian for N=2 supergravity

Application to supersymmetry breaking scenarios

Facilitation of black-hole solution studies

Abstract

Relying on the geometrical set up of Special K\"ahler Geometry and Quaternionic Geometry, which I discussed at length in my Lectures at the 1995 edition of this Spring School, I present here the recently obtained fully general form of N=2 supergravity with completely arbitrary couplings. This lagrangian has already been used in the literature to obtain various results: notably the partial breaking of supersymmetry and various extremal black--hole solutions. My emphasis, however, is only on providing the reader with a completely explicit and ready to use component expression of the supergravity action. All the details of the derivation are omitted but all the definitions of the items entering the lagrangian and the supersymmetry transformation rules are given.