Vacua of N=2 gauged supergravity derived from non-homogeneous quaternionic spaces
Klaus Behrndt, Gianguido Dall'Agata
TL;DR
Behrndt and Dall'Agata construct a family of 4D non-homogeneous quaternionic spaces that interpolate between AdS$_4$-like and SU$(2,1)$/U$(2)$ geometries, featuring two disjoint positive-definite regions separated by a timelike singularity and admitting four isometries suitable for Abelian gauging. Using 5D ${\cal N}=2$ gauged supergravity with hypermultiplets, they derive first-order domain-wall flows driven by the superpotential $W$ and analyze how the gauged isometries yield different vacuum structures in the two regions. They characterize all possible critical points, showing that in the κ=1 sector two IR points lie on the boundary and can be connected by a smooth domain-wall solution, explicitly constructed for a particular gauging, with a warp factor $e^{2U}$ that decays on both sides and traps gravity. The results open avenues for extensions to non-Abelian gaugings and for embedding these spaces in string/M-theory contexts, potentially yielding new brane-world and holographic insights.
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.