The fate of stringy AdS vacua and the WGC

TL;DR

The paper argues that non-supersymmetric AdS vacua arising in string theory are generically unstable due to a universal, perturbative channel that originates from the coupling between open (brane) and closed string sectors, in line with a strengthened WGC. It presents a brane–flux dual description of AdS vacua and proposes an effective $D$-dimensional gauged supergravity with $N$ vector multiplets to capture the open-string tachyonic channel at finite $N$. If valid, these results place strong constraints on non-supersymmetric holographic constructions and have implications for de Sitter scenarios and the broader string landscape. The work highlights the importance of including open-string dynamics in UV completions and suggests concrete avenues for testing the framework in explicit models.

Abstract

The authors of arXiv:1610.01533 have recently proposed a stronger version of the weak gravity conjecture (WGC), based on which they concluded that all those non-supersymmetric AdS vacua that can be embedded within a constistent theory of quantum gravity necessarily develop instabilities. In this paper we further elaborate on this proposal by arguing that the aforementioned instabilities have a perturbative nature and arise from the crucial interplay between the closed and the open string sectors of the theory.

Figures (5)

• Figure 1: In the brane picture, a given brane system that looks like a DW within the $D$-dimensional theory, may give rise to an AdS$_D$ vacuum in its near-horizon limit. Furthermore, as discussed in Kounnas:2007dd, extra spacetime-filling objects could be required for consistency. In the flux picture, such an AdS vacuum can be obtained from a compactification supported by $p$-form fluxes wrapping cycles of the internal manifold. Each of these fluxes is sourced by a corresponding extended object in the brane picture. Possible flux tadpoles are in correspondence with spacetime-filling sources.
• Figure 2: The causal structure of an extremal RN black hole. The oscillatory motion of a free-falling observer around the horizon (dotted timelike curve $\gamma$) necessarily would connect the two universes U & U$^\prime$ through the wormhole W and this structure repeats itself infinitely.
• Figure 3: The example of an initial data surface $\Sigma_0$ for a charged scalar field in the extremal RN geometry. It may be noted that these surfaces are universally incomplete Kunduri:2013ana.
• Figure 4: An artist's impression of the difference between supersymmetric (left) and non-supersymmetric (right) AdS vacua as they are constructed in the brane picture. The thick static DW separating them contains all the information concerning the branes which are not spacetime-filling. Note that the brane/anti-brane annihilation process may perturbatively occur on the right side of this picture only upon including the open string degrees of freedom living on the $p$-branes.
• Figure 5: The effective gauged supergravity theory describing the coupling between the closed and open string sector of a given compactification. In the $N\,=\,0$ limit (left) AdS flux vacua are generically separated by static DW's and hence do not show instabilities. In the $N\,=\,\infty$ limit, one can adopt the description of spacetime-filling branes as probes. The actual calculation that shows the presence of a tachyon at a perturbative level is the one at finite $N$ in this picture, i.e. where no decoupling limit is accessible.