Anti-deSitter Vacua of Gauged Supergravities with 8 Supercharges

TL;DR

This paper studies supersymmetric vacua in gauged supergravity theories with 8 supercharges, showing that such models have at most one extremum per branch, which is either a maximum or minimum of the superpotential, preventing regular domain wall solutions.

Contribution

It demonstrates that in these supergravity models, each disconnected scalar manifold branch admits at most one extremum, which constrains the existence of domain wall solutions.

Findings

Each branch has at most one extremum of the superpotential.

Extrema are either local maxima or minima, not saddle points.

No regular domain walls interpolate between different extrema.

Abstract

We investigate supersymmetric extrema of Abelian gauged supergravity theories with non-trivial vector multiplets and 8 supercharges in four and five dimensions. The scalar fields of these models parameterize a manifold consisting of disconnected branches and restricting to the case where this manifold has a non-singular metric we show that on every branch there can be at most one extremum, which is a local maximum (for W>0) or a minimum (for W<0) of the superpotential W. Therefore, these supergravity models do not allow for regular domain wall solutions interpolating between different extrema of the superpotential and the space-time transverse to the wall asymptotically always approaches the boundary of AdS (UV-fixed points in a dual field theory).