AdS Euclidean wormholes

TL;DR

The work investigates asymptotically AdS Euclidean wormholes across simple low-energy models and UV-complete truncations, revealing a Hawking-Page-like phase structure with large and small wormhole branches in many cases. A central finding is that while large wormholes can be locally stable against field-theoretic negative modes, they typically suffer from brane-nucleation instabilities in UV-complete theories, suggesting additional lower-action disconnected saddles. In mass-deformed ABJM and Type IIB truncations, wormholes exist only in restricted parameter regimes and do not dominate, reinforcing the view that factorization in AdS/CFT remains nontrivial and potentially ensemble-based. The study provides a unified stability framework across models, clarifying when wormholes can influence boundary-ensemble interpretations and highlighting the persistent challenge of brane-induced instabilities in UV-complete settings.

Abstract

We explore the construction and stability of asymptotically anti-de Sitter Euclidean wormholes in a variety of models. In simple ad hoc low-energy models, it is not hard to construct two-boundary Euclidean wormholes that dominate over disconnected solutions and which are stable (lacking negative modes) in the usual sense of Euclidean quantum gravity. Indeed, the structure of such solutions turns out to strongly resemble that of the Hawking-Page phase transition for AdS-Schwarzschild black holes, in that for boundary sources above some threshold we find both a `large' and a `small' branch of wormhole solutions with the latter being stable and dominating over the disconnected solution for large enough sources. We are also able to construct two-boundary Euclidean wormholes in a variety of string compactifications that dominate over the disconnected solutions we find and that are stable with respect to field-theoretic perturbations. However, as in classic examples investigated by Maldacena and Maoz, the wormholes in these UV-complete settings always suffer from brane-nucleation instabilities (even when sources that one might hope would stabilize such instabilities are tuned to large values). This indicates the existence of additional disconnected solutions with lower action. We discuss the significance of such results for the factorization problem of AdS/CFT.

Figures (16)

• Figure 1: An example showing failure of factorization due to spacetime wormholes. The top line represents a path integral $\langle Z\rangle$. Although we have drawn the configuration as connected, it may include contributions from disconnected spacetimes as well. In any case, the natural path integral $\langle Z^2 \rangle$ associated with a pair of boundaries yields all terms generated by squaring $\langle Z\rangle$, but also contains additional contributions connecting the two boundaries as indicated by the second term in the bottom line.
• Figure 2: The source for the Maxwell fields $A^{(I)}$$\Phi_0$ as a function of $\Phi_{\star}$. There is a minimum value of $\Phi_0$, $\Phi_0^{\min}\approx 3.563349$, above which two types of wormhole solutions exist.
• Figure 3: Radius of the wormhole solutions as a function of the Maxwell source $\Phi_0$. For fixed value of $\Phi_0>\Phi_0^{\min}$ two wormhole solutions exist.
• Figure 4: The difference in Euclidean action between the disconnected and connected solutions. At any $\Phi_0$, the larger value of $\Delta S_{U(1)^3}$ corresponds to the large wormhole and the smaller value corresponds to the small wormhole. Due to the similarity to the familiar Hawking-Page transition, we use $\Phi_{\mathrm{HP}}$ to denote the value of $\Phi_0$ at which $\Delta S_{U(1)^3}=0$ for the large wormhole. For $\Phi_0>\Phi_{\mathrm{HP}}$, the large wormhole solution becomes dominant while the small wormhole solution is always subdominant.
• Figure 5: The homogeneous negative mode with $\ell=0$ as a function of the black hole radius, measured in units of $r_0^{\min}$. At $r=r_0^{\min}$ the negative mode vanishes, and becomes positive thereafter.