N=2 Supergravity Lagrangian Coupled to Tensor Multiplets with Electric and Magnetic Fluxes

TL;DR

This work derives a complete four-dimensional $N=2$ supergravity Lagrangian that couples vector multiplets to a scalar–tensor sector in the presence of electric and magnetic fluxes, with a symplectic-invariant scalar potential. It achieves this by combining magnetic mass–shifts (FI terms) with an additional electric mass–shift in the fermionic transformations and employing a rheonomic construction to preserve supersymmetry, yielding a Lagrangian that remains covariant under symplectic transformations. The scalar potential is a quadratic form in the mass shifts and remains symplectic-invariant, reproducing known Calabi–Yau flux compactification potentials in appropriate limits, and supports a semisimple gauging of the scalar-tensor sector. The results provide a unified 4D framework for Type II flux compactifications with both R-R and NS-NS fluxes, clarifying the role of the generalized tadpole constraint and the pairing of electric and magnetic charges in a symplectic structure.

Abstract

We derive the full N=2 supergravity Lagrangian which contains a symplectic invariant scalar potential in terms of electric and magnetic charges. As shown in reference [1], the appearance of magnetic charges is allowed only if tensor multiplets are present and a suitable Fayet-Iliopoulos term is included in the fermion transformation laws. We generalize the procedure in the quoted reference by adding further a Fayet-Iliopoulos term which allows the introduction of electric charges in such a way that the potential and the equations of motion of the theory are symplectic invariant. The theory is further generalized to include an ordinary electric gauging and the form of the resulting scalar potential is given.