D=4, N=2 Gauged Supergravity in the Presence of Tensor Multiplets

TL;DR

The paper extends four-dimensional $D=4$, ${\cal N}=2$ supergravity by including tensor multiplets and their couplings to vector multiplets, using a superspace framework. It dualizes selected hypermultiplet scalars into tensor fields, yielding a reduced quaternionic–Kähler geometry and a scalar–tensor multiplet sector, and analyzes electric and magnetic gaugings with mass parameters $m^{I\Lambda}$. The resulting scalar potential splits into a symplectic invariant part and a noninvariant part, with some Abelian gaugings reducible to the standard ${\cal N}=2$ form and nonabelian gaugings giving genuine deformations; magnetic couplings are interpreted via magnetic Killing vectors. The construction clarifies connections to flux compactifications of type II string theories and reveals new consistency conditions for tensor-containing ${\cal N}=2$ supergravities relevant to string/M-theory compactifications. These results provide a systematic framework for tensor-containing ${\cal N}=2$ supergravities that could arise in string/M-theory compactifications.

Abstract

Using superspace techniques we construct the general theory describing D=4, N=2 supergravity coupled to an arbitrary number of vector and scalar--tensor multiplets. The scalar manifold of the theory is the direct product of a special Kaehler and a reduction of a Quaternionic-Kaehler manifold. We perform the electric gauging of a subgroup of the isometries of such manifold as well as ``magnetic'' deformations of the theory discussing the consistency conditions arising in this process. The resulting scalar potential is the sum of a symplectic invariant part (which in some instances can be recast into the standard form of the gauged N =2 theory) and of a non--invariant part, both giving new deformations. We also show the relation of such theories to flux ompactifications of type II string theories.