On The Stability Of Non-Supersymmetric AdS Vacua

TL;DR

This work constructs two infinite families of non-supersymmetric $AdS_4$ vacua in massive IIA flux compactifications on a blown-up Calabi–Yau, demonstrates perturbative stability of Type 2 and Type 3 vacua, and analyzes their non-perturbative stability against decays to other vacua. It shows, via Coleman–De Luccia thin-wall analysis and D4-brane domain walls, that many decays are forbidden because the domain-wall tension cannot be sufficiently small relative to the AdS energy difference; Type 2 vacua are at best marginally unstable, while Type 3 vacua admit some decays to other vacua. A crucial pairing symmetry relates Type 2 vacua to SUSY partners with the same energy, providing a mechanism for their stability within the approximations, and Appendix D discusses an approximate symmetry extending this idea. Overall, the results suggest that metastable non-supersymmetric AdS vacua—and possibly dual CFTs—may be more robust in flux compactifications than naively expected, though subleading effects and broader vacuum scans remain to be explored.

Abstract

We consider two infinite families of Non-Supersymmetric $AdS_4$ vacua, called Type 2) and Type 3) vacua, that arise in massive IIA supergravity with flux. We show that both families are perturbatively stable. We then examine non-perturbative decays of these vacua to other supersymmetric and non-supersymmetric $AdS_4$ vacua mediated by instantons in the thin wall approximation. We find that many decays are ruled out since the tension of the interpolating domain wall is too big compared to the energy difference in AdS units. In fact, within our approximations no decays of Type 2) vacua are allowed, although some decays are only marginally forbidden. This can be understood in terms of a "pairing symmetry" in the landscape which relate Type 2) vacua with supersymmetric ones of the same energy.