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

TL;DR

This work extends Euclidean axion wormholes to AdS$_3$ by treating the axion as a dual $U(1)$ gauge field and constructs classical wormhole solutions with spherical, toroidal, and hyperbolic cross-sections. Using the ADM formalism, it demonstrates regularity and perturbative stability for these saddles via a vector-sector SVT analysis, showing nonzero-mode perturbations are positive and that torus zero-modes are eliminated by boundary conditions that fix the field strength. The authors compute the Euclidean action for torus and sphere wormholes, finding explicit expressions and asymptotic behavior in terms of the throat size $\tau_{ ext{min}}$, AdS length $l$, and charges $n$, while hyperbolic quotients are left for future work. The results imply stable wormhole contributions to the 3D gravitational path integral in AdS$_3$, motivating further study of UV completions, potential phenomenology for AdS$_3$/CFT$_2$, and the interplay with factorization and cluster-decomposition in holography.

Abstract

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.

Figures (1)

• Figure 1: Three wormhole geometries considered in this paper. The first is the half wormhole solution found as a solution of the Euclidean equations of motion which has a minimal value of $\tau$, and can be thought of as related to the amplitude for emission of a "baby universe". The second is a two boundary wormhole made from "gluing" two half solutions together. The third is a single boundary wormhole which comes from identifying the boundaries of the two boundary solution, which is for large mouth separation asymptotically a solution to the equation of motion with the same action as the two boundary solution, in the sense of an instanton gas approximation. All of this is explained nicely in the review Hebecker:2018ofv from which we borrowed this illustration.