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arxiv: 2504.10868 · v3 · pith:3NC3FL7Wnew · submitted 2025-04-15 · ✦ hep-th

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

Andrew Loveridge , Hao-Yu Sun This is my paper

Pith reviewed 2026-05-22 20:38 UTC · model grok-4.3

classification ✦ hep-th
keywords AdS3axion wormholesEuclidean path integralGiddings-Strominger wormholeswormhole stabilityU(1) gauge fieldgravitational instantons
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0 comments X

The pith

Euclidean axion wormholes in AdS3 remain regular and stable for arbitrary mouth-to-AdS radius ratios and multiple topologies.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs explicit classical solutions for axion wormholes in three-dimensional anti-de Sitter space. These solutions are shown to be regular and stable under perturbations. The authors compute the Euclidean actions for any ratio of wormhole mouth radius to the AdS radius and for different spatial topologies. The work generalizes prior flat-space results by using the equivalence of the axion to a U(1) gauge field in AdS3, and discusses how these stable configurations should enter the gravitational path integral.

Core claim

Classical Euclidean Giddings-Strominger axion wormholes exist in AdS3, are regular and stable, and have finite, computable actions that hold for arbitrary ratios of the wormhole mouth radius to the AdS radius and across various topologies, allowing them to contribute to the Euclidean gravitational path integral.

What carries the argument

The Euclidean wormhole ansatz carried over from flat space using the axion-U(1) gauge field equivalence in AdS3, which produces metric and field solutions satisfying the equations of motion.

Load-bearing premise

The axion can be treated as equivalent to a U(1) gauge field in AdS3 without introducing extra instabilities or singularities in the Euclidean geometry.

What would settle it

A calculation that finds a negative mode in the second variation of the action around one of the constructed wormhole solutions would falsify the stability result.

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript generalizes results on stable Euclidean Giddings-Strominger axion wormholes from asymptotically flat 4D spacetime to AdS3, where the axion is dual to a U(1) gauge field. It claims to explicitly construct the classical wormhole solutions, verify their regularity and stability, compute the on-shell Euclidean actions for arbitrary ratios of wormhole mouth radius to AdS radius and across various topologies, and discuss implications for the 3D gravitational path integral.

Significance. If the stability holds after imposing AdS3 boundary conditions, the explicit constructions and action computations for continuous parameter ranges would supply a controlled, lower-dimensional laboratory for studying wormhole contributions to the Euclidean path integral, including potential effects on factorization. The ability to vary the radius ratio and topology is a concrete strength that could allow falsifiable statements about when such saddles dominate.

major comments (1)
  1. [Stability analysis (presumably the section following the classical solutions)] The central stability claim rests on carrying over the flat-space wormhole ansatz via the axion-U(1) equivalence. However, AdS3 fixes the asymptotic behavior of the gauge field at the AdS boundary; this can source additional gravitational and gauge fluctuation modes whose quadratic action is not guaranteed to be positive. The manuscript must demonstrate explicitly (via the eigenvalue spectrum of the second variation) that no negative modes appear for the considered radius ratios and topologies after these boundary conditions are imposed.
minor comments (1)
  1. [Abstract] The abstract states that actions are computed 'for arbitrary ratios' but does not indicate the range of validity or any singularities encountered at extreme ratios; a brief statement of the domain should be added.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We address the major comment below.

read point-by-point responses

  1. Referee: [Stability analysis (presumably the section following the classical solutions)] The central stability claim rests on carrying over the flat-space wormhole ansatz via the axion-U(1) equivalence. However, AdS3 fixes the asymptotic behavior of the gauge field at the AdS boundary; this can source additional gravitational and gauge fluctuation modes whose quadratic action is not guaranteed to be positive. The manuscript must demonstrate explicitly (via the eigenvalue spectrum of the second variation) that no negative modes appear for the considered radius ratios and topologies after these boundary conditions are imposed.

    Authors: We agree that an explicit verification of the fluctuation spectrum under AdS3 boundary conditions is required to fully substantiate the stability claim. The manuscript establishes regularity and stability by constructing the classical solutions via the axion-U(1) duality and generalizing the known flat-space result, with the bulk quadratic action taking an analogous form. However, the fixed gauge-field asymptotics in AdS3 were not subjected to a dedicated eigenvalue analysis in the current text. We will revise the stability section (and add supporting material if needed) to compute the spectrum of the second variation operator for metric and gauge perturbations, imposing the standard AdS3 boundary conditions, and demonstrate the absence of negative modes for the full range of mouth-to-AdS radius ratios and topologies considered. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper explicitly constructs classical wormhole solutions in AdS3, verifies regularity and stability via direct analysis of the metric and field equations, and computes the Euclidean actions from those solutions for arbitrary mouth-to-AdS radius ratios and topologies. These steps are independent calculations that do not reduce to fitted parameters renamed as predictions, self-definitional equivalences, or load-bearing self-citations. The axion-U(1) equivalence is invoked only to motivate carrying over the flat-space ansatz; the new AdS3 results are derived separately and presented as such. No quoted equation or claim collapses to its own input by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard Euclidean gravity action plus the domain assumption that the axion is dual to a U(1) gauge field; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The axion is equivalent to a U(1) gauge field in AdS3.
    Explicitly invoked in the abstract to justify carrying over the wormhole ansatz.

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