Vacua of N=2 gauged supergravity derived from non-homogeneous quaternionic spaces

TL;DR

This paper explores a class of non-homogeneous quaternionic spaces in 4D supergravity, revealing their structure, isometries, and the nature of domain wall solutions, including singular and smooth interpolations between critical points.

Contribution

It introduces a new class of non-homogeneous quaternionic spaces and analyzes their supergravity gauging and domain wall solutions, highlighting differences from known homogeneous spaces.

Findings

Two regions with positive definite metrics separated by a non-physical region.

Existence of singular domain walls in one region.

Smooth domain wall connecting two IR critical points on the boundary.

Abstract

We discuss a class of 4-dimensional non-homogeneous quaternionic spaces, which become the two known homogeneous spaces (EAdS_4$ and SU(2,1)/U(2)) in certain limits. These moduli spaces have two regions where the metric is positive definite, separated by a non-physical region where the metric has timelike directions and which contains a curvature singularity. They admit four isometries and we consider their general Abelian gauging. The critical points of the resulting superpotential and hence the possible domain wall solutions differ significantly in the two regions. On one side one can construct only singular walls, whereas in the other we found a smooth domain wall interpolating between two infra-red critical points located exactly on the boundary of the physical allowed parameter region.