Curved BPS domain wall solutions in four-dimensional N=2 supergravity

TL;DR

The authors construct curved 4D N=2 gauged supergravity domain wall solutions arising from two Abelian gaugings: gauging a U(1) within the SU(2) R-symmetry or gaugings of a universal hypermultiplet isometry. They show that vector multiplet scalars follow attractor equations identical to those in ungauged N=2 black holes, while hypermultiplets are either constant (s=0) or exhibit run-away behavior (s=2). The resulting domain walls are generally curved, with a 3D cosmological constant determined by a symplectic one-form, and display a precise correspondence with black-hole data via the underlying symplectic structure. The work connects to string theory via H-fluxes and brane constructions, and outlines avenues for including more general gaugings and dilaton-stabilizing potentials.

Abstract

We construct four-dimensional domain wall solutions of N=2 gauged supergravity coupled to vector and to hypermultiplets. The gauged supergravity theories that we consider are obtained by performing two types of Abelian gauging. In both cases we find that the behaviour of the scalar fields belonging to the vector multiplets is governed by the so-called attractor equations known from the study of BPS black hole solutions in ungauged N=2 supergravity theories. The scalar fields belonging to the hypermultiplets, on the other hand, are either constant or exhibit a run-away behaviour. These domain wall solutions preserve 1/2 of supersymmetry and they are, in general, curved. We briefly comment on the amount of supersymmetry preserved by domain wall solutions in gauged supergravity theories obtained by more general gaugings.