On AdS$_7$ stability

TL;DR

This paper investigates the stability of non-supersymmetric AdS7 solutions in type IIA supergravity, revealing perturbative stability in some sectors but non-perturbative decay via NS5 bubbles for most solutions.

Contribution

It provides a comprehensive stability analysis of non-supersymmetric AdS7 solutions, combining KK spectrum analysis, supergravity, and brane polarization techniques to identify instabilities.

Findings

KK spectrum shows no perturbative instabilities.

Most non-supersymmetric solutions are unstable due to scalar modes.

NS5 bubbles induce non-perturbative decay in remaining solutions.

Abstract

AdS$_7$ supersymmetric solutions in type IIA have been classified, and they are infinitely many. Moreover, every such solution has a non-supersymmetric sister. In this paper, we study the perturbative and non-perturbative stability of these non-supersymmetric solutions, focusing on cases without orientifolds. Perturbatively, we first look at the KK spectrum of spin-2 excitations. This does not exhibit instabilities, but it does show that there is no separation of scales for either the BPS and the non-BPS case, thus proving for supersymmetric AdS$_7$ a well-known recent conjecture. We then use 7d gauged supergravity and a brane polarization computation to access part of the spectrum of KK scalars. The result signals an instability for all non-supersymmetric solutions except those that have a single D8 on each side. We finally look at non-perturbative instabilities, and find that NS5 bubbles make these remaining solutions decay.