General Matter Coupled N=2 Supergravity

TL;DR

This paper presents a comprehensive, coordinate-independent formulation of N=2 supergravity coupled to various matter multiplets, including the full Lagrangian and supersymmetry variations, facilitating the study of such theories in a broad geometric context.

Contribution

It introduces a manifestly symplectic covariant formalism for N=2 supergravity with matter couplings, extending previous results and enabling analysis in more general geometric settings.

Findings

Complete Lagrangian and supersymmetry variations provided.

Scalar potential formulated for arbitrary quaternionic and special geometry.

Formalism applicable to a wide class of N=2 supergravity theories.

Abstract

The general form of N=2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets, with a generic gauging of the scalar manifold isometries is given. This extends the results already available in the literature in that we use a coordinate independent and manifestly symplectic covariant formalism which allows to cover theories difficult to formulate within superspace or tensor calculus approach. We provide the complete lagrangian and supersymmetry variations with all fermionic terms, and the form of the scalar potential for arbitrary quaternionic manifolds and special geometry, not necessarily in special coordinates. Our results can be used to explore properties of theories admitting $N=2$ supergravity as low energy limit.