Universal isolation in the AdS landscape

TL;DR

The paper addresses whether perturbatively stable AdS vacua remain non-perturbatively stable against bubble nucleation in quantum gravity. It develops a universal criterion based on fake supersymmetry and the Hamilton-Jacobi formalism, expressing the scalar potential through a global fake superpotential $f$ and leveraging the BF bound to guarantee stability when a global bounding function exists. Two explicit string-inspired AdS landscapes (AdS$_7\times S^3$ and AdS$_4\times S^3\times S^3$) are analyzed, showing that all BF-respecting vacua admit global $f$ functions and static domain walls that prevent tunneling, supporting a broader conjecture of universal non-perturbative isolation in the AdS landscape. The work connects non-perturbative stability to holographic RG flows and suggests a general, model-independent mechanism for stability in consistent quantum gravity, with potential extensions to other AdS vacua.

Abstract

We study the universal conditions for quantum non-perturbative stability against bubble nucleation for pertubatively stable AdS vacua based on positive energy theorems. We also compare our analysis with the pre-existing ones in the literature carried out within the thin-wall approximation. The aforementioned criterion is then tested in two explicit examples describing massive type IIA string theory compactified on $S^3$ and $S^3\,\times\,S^3$, respectively. The AdS landscape of both classes of compactifications is known to consist of a set of isolated points. The main result is that all critical points respecting the Breitenlohner-Freedaman (BF) bound also turn out be stable at a non-perturbative level. Finally, we speculate on the possible universal features that may be extracted from the above specific examples.

Figures (7)

• Figure 1: The three different situations that may occur in presence of a local AdS maximum and a local AdS minum. Left: Both points obey the positive energy theorem and are hence stable against bubble nucleation. Middle: The maximum turns unstable and decays towards the minimum, which instead stays non-perturbatively stable. Right: Both the maximum and the minimum exhibit non-perturbative instabilities.
• Figure 2: The three different situations that may occur in presence of two local AdS minima separated by an unstable maximum. Left: Both points obey the positive energy theorem and are hence stable against bubble nucleation. Middle: The higher minimum turns unstable and decays towards the deeper minimum, which instead stays non-perturbatively stable. Right: Both minima violate the hypothesis of the positive energy theorem and still, the conclusion stays identical to the 2b case.
• Figure 3: The non-perturbative stability of massive type IIA on $\textrm{AdS}_{7}\times S^{3}$ models summarized. The blue curve shows the profile of the scalar potential \ref{['V_ISO3']}, with a non-supersymmetric local minimum (left) and a supersymmetric local maximum (right). From both points there starts a globally bounding function $-\frac{3}{5}\,f^2$ ensuring their non-perturbative stability (curves in red & brown, respectively). Note that these branches only cross at one point and respecting crossing rule nr. 2. This exactly realizes Situation 1a in figure \ref{['fig:AdSlandscape_1']}. Finally, the green curve represents the bounding function defining the static DW (zoomed in on the right).
• Figure 4: The non-perturbative stability of massive type IIA on $\textrm{AdS}_{4}\times S^{3}\times S^{3}$ models summarized. The above sheet represents the profile of the scalar potential \ref{['V_ISO3']} in a particular two-dimensional slice of the scalar manifold, with a supersymmetric local extremum on the left and two additional non-supersymmetric ones (Sol. 3 & 4 in table \ref{['table:AdS4']}). From all points there starts a globally bounding function $-3\,f^2$ ensuring their non-perturbative stability (represented by the paraboloids peaked at each critical point).
• Figure 5: The profile of the six real scalars in our STU-model along the flow representing the static DW interpolating between Sol. 4 & Sol. 1.