General Matter Coupled N=2 Supergravity

TL;DR

This work provides a completely general framework for $N=2$ supergravity coupled to arbitrary vector and hypermultiplets with gauged isometries, using a coordinate-free, symplectic covariant approach that does not require a prepotential $F(X)$. It delivers the full Lagrangian and supersymmetry transformation rules in terms of purely geometric data from special Kähler and quaternionic geometries, and derives a symplectic-invariant expression for the scalar potential valid for arbitrary geometry not necessarily in special coordinates. The key contributions include the explicit Lagrangian, fermionic shifts, and mass matrices, along with a general scalar potential formula and a discussion of Fayet–Iliopoulos terms and SUSY-breaking patterns, enabling analysis of low-energy limits and string-theory motivated scenarios. Overall, the paper unifies the treatment of gauged $N=2$ theories with matter, broadening the scope of models accessible for phenomenology and cosmology in supergravity and string contexts.

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.