AdS3 axion wormholes as stable contributions to the Euclidean gravitational path integral

Recent work has demonstrated that Euclidean Giddings-Strominger axion wormholes are stable in asymptotically flat 4D Minkowski spacetime, suggesting that they should, at least naively, be included as contributions in the quantum gravitational path integral. Such inclusion appears to lead to known wormhole paradoxes, such as the factorization problem. In this paper, we generalize these results to AdS3 spacetime, where the axion is equivalent to a U(1) gauge field. We explicitly construct the classical wormhole solutions, show their regularity and stability, and compute their actions for arbitrary ratios of the wormhole mouth radius to the AdS radius and across various topologies. Finally, We discuss potential implications of these findings for the 3D gravitational path integral.

💡 Research Summary

This paper investigates the existence, stability, and implications of Euclidean axion wormholes in three-dimensional anti-de Sitter (AdS3) spacetime. Motivated by the long-standing tension in quantum gravity between background independence (which suggests summing over all topologies) and locality/unitarity (which is threatened by wormhole contributions), the authors generalize prior results from four-dimensional flat space to the holographically significant AdS3 context.

The core of the work begins by constructing classical wormhole solutions. In three dimensions, the axion field responsible for sourcing the Giddings-Strominger wormhole is equivalent to a U(1) gauge field (a dual photon), simplifying the analysis. Using the ADM formalism and a minisuperspace approach, the authors derive explicit solutions for spatial cross-sections with spherical (S^2), toroidal (T^2), and compact hyperbolic (H^2/Γ) topologies. Initially, the metric in a radial coordinate τ exhibits a coordinate singularity at a minimum radius τ_min. By introducing a new coordinate T, defined such that τ^2 = T^2 + τ_min^2, they obtain a completely smooth, two-sided wormhole geometry where T runs from -∞ to ∞. The regularity of these solutions is confirmed by showing the finiteness of curvature invariants and the gauge field strength everywhere, provided the magnetic flux (axion charge) n is non-zero.

The paper then meticulously analyzes the stability of these solutions, which is crucial for determining whether they constitute valid saddle points in the Euclidean gravitational path integral. In three dimensions, there are no propagating bulk gravitons, so the analysis focuses on perturbations of the U(1) field and their gravitational backreaction. Employing an SVT (scalar-vector-tensor) decomposition and choosing convenient gauges (Coulomb gauge for the gauge field, vector gauge for gravity), the authors reduce the dynamical degrees of freedom to a divergence-free vector perturbation of the gauge potential and a non-dynamical shift vector perturbation. They demonstrate that under boundary conditions which fix the axion charge and the boundary metric—the natural choice for defining the path integral—the wormhole solutions are stable. Any zero modes identified correspond to symmetries (like translations of the wormhole throat) and do not indicate dynamical instability. This result extends the stability conclusion of earlier work in 4D flat space to AdS3 and across different topologies.

Subsequently, the authors compute the Euclidean action for these wormholes. The action is expressed explicitly as a function of the ratio of the wormhole mouth size to the AdS radius (τ_min/l) and the topological properties (Euler characteristic χ, volume V) of the spatial cross-section. This calculation is essential for evaluating the relative weight of these saddle points in the path integral.

Finally, the discussion section explores the significant implications of these findings. The demonstration that stable wormholes exist in AdS3 suggests they should, at least naively, be included in the gravitational path integral. This inclusion notoriously leads to the “factorization problem” in the context of AdS/CFT: the contributions from wormholes connecting two asymptotic boundaries prevent the partition function from factorizing into a product of partition functions for each boundary, seemingly violating basic principles of a local holographic dual. The paper thus sharpens a fundamental conflict in quantum gravity between the principle of background independence (summing over topologies) and the requirements of locality and unitarity as understood through holography. The authors conclude by suggesting future work to determine if these wormhole saddles dominate the path integral, if they might be suppressed by other non-perturbative effects, or how their status might change in a full string theory embedding with additional fields.