Non-supersymmetric AdS instability conjecture

Fix a spacetime dimension $d\ge 3$ and a standalone ultraviolet-complete quantum-gravity theory: the complete gravitational system, rather than an effective solution or a localized subsystem whose consistency requires a higher-dimensional gravitational host. Supply its proposed low-energy Einstein-gravity description, matter content, validity regime and completion assumptions. A $d$-dimensional anti-de Sitter (AdS) spacetime here has Lorentzian metric with constant sectional curvature $-L_{\mathrm{A}\mathrm{d}\mathrm{S}}^{-2}<0$, namely $R_{\mu \nu \rho \sigma }=-L_{\mathrm{A}\mathrm{d}\mathrm{S}}^{-2}(g_{\mu \rho }{g}_{\nu \sigma }-g_{\mu \sigma }{g}_{\nu \rho })$; global quotients, topology and boundary conditions are part of the vacuum data. A vacuum here is a specified solution of the declared field equations with AdS-invariant background fields. “Non-supersymmetric” means that no nonzero supersymmetry parameter obeying the declared boundary conditions makes all field variations vanish on this solution; the transformation equations are supplied with the theory. Require AdS-supporting flux: in the effective $d$-dimensional description there is an AdS-filling field strength $F_d=q{\mathrm{v}\mathrm{o}\mathrm{l}}_g$ with $q\mathrm{\ne }0$, or a specified equivalent dual description, whose stress tensor participates in the vacuum field equations. The form degree, normalization and quantization law, including the integration cycle of the flux or dual flux, are fixed data. A merely nonzero spectator flux is insufficient. An Einstein-gravity description here includes the $d$-dimensional Einstein-frame gravitational term $M_{P,d}^{d-2}R\mathrm{/}2$ with a finite number of retained matter fields and declared flux sectors; all omitted modes and corrections have a stated control regime. An allowed charged-brane decay channel is a brane configuration with declared charge, tension/action, boundary behavior and finite-action nucleation process compatible with the flux transition. Call the vacuum unstable in this question if such a channel is physically allowed under the fixed boundary conditions. For such a vacuum of the specified ultraviolet-complete theory, non-supersymmetric and supported by quantized form flux in the declared finite-matter Einstein-gravity regime, is there always an allowed channel that makes it unstable? Ooguri–Vafa propose this flux-supported instability using a strengthened weak-gravity premise; their separate conjecture that non-supersymmetric anti-de Sitter/conformal-field-theory holography is impossible for finite-matter Einstein gravity is broader and is not merged into this item.

The ultraviolet-completion condition is a hypothesis on the class, not a claim that any chosen Einstein-gravity solution has such a completion. The strengthened weak-gravity premise motivates the proposed instability and is not established here or used as an accepted proof supplier. The Einstein-gravity regime and included nonperturbative channels must be declared. A formal charge bound alone does not establish a decay solution. The narrow flux-supported instability is distinct from the paper’s broader proposed absence of non-supersymmetric anti-de Sitter/conformal-field-theory duals with a finite-matter Einstein-gravity description.

Scalar, gauge and theory-family data for swampland conjectures

Ooguri–Vafa, pp. 1–4

Status review dated 2025-09-05: the bounded record for the narrow flux-supported claim is Ooguri–Vafa, PDF pp. 1–4, and Lehnert, §II.L, PDF pp. 69–71. Lehnert describes brane nucleation as a conditional mechanism when a charged brane’s charge exceeds its tension, derived from the sharpened weak-gravity premise; it then distinguishes the broader no-non-supersymmetric-theories proposal. Neither source proves that every vacuum in this stated class has an allowed decay channel. Lehnert states that its reviewed literature was published before 2025 (PDF p. 2, note 8). This item makes no status claim about literature after that cutoff and does not claim an exhaustive search.