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

TL;DR

This paper constructs curved BPS domain wall solutions in four-dimensional N=2 gauged supergravity, revealing how scalar fields behave under different gaugings and preserving half of the supersymmetry.

Contribution

It provides explicit curved domain wall solutions in N=2 gauged supergravity with novel scalar field behaviors linked to attractor equations.

Findings

Scalar fields in vector multiplets follow attractor equations.

Hypermultiplet scalars are either constant or run-away.

Solutions preserve 1/2 supersymmetry and are generally curved.

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.