arxiv: 2605.11081 · v1 · submitted 2026-05-11 · ✦ hep-th · hep-ph

Recognition: no theorem link

Compact space catalysis of false vacuum decay and Schwinger effect

Saquib Hassan , John March-Russell

Authors on Pith no claims yet

Pith reviewed 2026-05-13 03:18 UTC · model grok-4.3

classification ✦ hep-th hep-ph

keywords false vacuum decaycompact spacebounce solutionsColeman bubbleSchwinger effectaxion electrodynamicsvacuum stability

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The pith

In compact spaces below a critical volume, false vacuum decay is mediated by a new homogeneous bounce rather than the Coleman bubble, typically enhancing the decay rate.

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

The paper studies false vacuum decay at zero temperature when spatial dimensions are compactified to finite volume. It shows that below a critical size the standard O(D)-symmetric bubble of Coleman ceases to be the lowest-action decay path; a distinct bounce solution appears instead. This new bounce, when continued to real time, nucleates a spatially homogeneous field configuration for the smallest volumes and a nearly homogeneous one for volumes just above the threshold. The result applies both to ordinary scalar potentials and to a compact-space version of axion electrodynamics that parallels the Schwinger effect.

Core claim

For volumes below a critical value in D compact spatial dimensions, false vacuum decay proceeds through a new bounce solution distinct from the O(D) bubble. Upon analytic continuation this bounce nucleates a homogeneous field configuration for sub-critical volumes and quasi-homogeneous configurations for slightly larger ones; it is not a thin- or thick-walled bubble sitting in false vacuum. The bounce possesses the required negative-mode spectrum to describe false vacuum decay and yields an exponentially larger decay rate than the Coleman solution in the relevant regime.

What carries the argument

The new compact-space bounce obtained by solving the Euclidean equations of motion on a finite-volume manifold; it replaces the Coleman O(D) bubble as the dominant saddle for decay when the spatial volume falls below a critical threshold.

If this is right

Decay rates become exponentially larger than Coleman predictions for sufficiently small compact volumes.
Nucleation produces a homogeneous or quasi-homogeneous field state rather than an isolated bubble.
A continuous cross-over occurs from fully homogeneous to quasi-homogeneous solutions as volume grows past the critical value.
The same bounce governs an enhanced analog of the Schwinger effect in compact (1+1)-dimensional axion electrodynamics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Models of the early universe or particle physics that invoke compact extra dimensions may need revised vacuum-lifetime estimates.
Real-time simulations of scalar fields on small tori could directly observe the homogeneous nucleation process predicted by the bounce.

Load-bearing premise

The newly identified bounce is the minimal-action saddle that controls the decay amplitude at small volumes, rather than some other field configuration or higher-order effect taking over.

What would settle it

Explicit numerical comparison of the Euclidean action of the new bounce versus the Coleman bubble for a concrete potential, confirming which action is smaller below the stated critical volume.

read the original abstract

We study zero-temperature false vacuum decay in $D$ compact spatial dimensions and show that for volumes below a critical value a new bounce solution, different from Coleman's celebrated $O(D)$ bubble, mediates the decay process, and typically leads to an exponentially enhanced decay rate. The bounce, when analytically continued to Lorentzian signature, nucleates a homogeneous field configuration for spatial volumes below a critical value, and quasi-homogeneous configurations for slightly larger volumes, and is not of the form of a thin or thick-walled bubble embedded in a false vacuum background. We explicitly show that the new bounce has the necessary features associated with false vacuum decay, following from its eigenvalue spectrum of fluctuations. The cross-over from homogeneous to quasi-homogeneous solutions as the spatial volume is increased is discussed, as is a real-time interpretation of the bounce. We apply this bounce to the study of a scalar field model, as well as a close cousin of the Schwinger effect that applies to $(1+1)d$ axion electrodynamics in compact space.

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.

Desk Editor's Note private letter to a colleague

Compact dimensions introduce a homogeneous bounce that dominates false vacuum decay below a critical volume, though explicit action comparisons are needed to confirm it is the minimal saddle.

read the letter

The main point is that false vacuum decay in compact spaces gets a new channel: a homogeneous bounce that takes over for small volumes and speeds things up a lot. The authors solve the Euclidean bounce equation on a compact manifold and identify this solution, which differs from the standard bubble. For the smallest volumes it is fully homogeneous, nucleating a uniform field configuration in real time. As volume grows, it turns quasi-homogeneous. They show the fluctuation operator has exactly one negative eigenvalue, as required for a decay process. The crossover is described, along with a Lorentzian interpretation. They work out examples in a scalar theory and in compact axion electrodynamics, which is a Schwinger analog. This is new work. The homogeneous bounce is not in the usual Coleman-De Luccia setup, and it emerges directly from the compact geometry without extra assumptions. The calculation looks clean on the derivation side. The critical volume comes out from the equations, and the applications are straightforward. Where it is softer is on proving this is the lowest-action saddle. The paper finds the solution and checks its local stability via the spectrum, but does not compare the action value to what the O(D) bubble would give when squeezed into the same compact space, or to multi-bounce or other paths. That comparison would nail down that nothing else undercuts it near the transition. The eigenvalue details are summarized rather than shown in full. This is worth attention from hep-th people doing vacuum stability in compactifications or cosmology. It could change how we estimate decay rates when dimensions are finite. A reader who knows the bounce formalism will get the most out of it. The paper should go to peer review; the idea is interesting and the math is there, even if some supporting checks would help.

Referee Report

3 major / 2 minor

Summary. The paper studies zero-temperature false vacuum decay in D compact spatial dimensions. It identifies a new bounce solution, distinct from Coleman's O(D) bubble, that mediates decay for spatial volumes below a critical value and yields an exponentially enhanced rate. Upon analytic continuation to Lorentzian signature, this bounce nucleates homogeneous field configurations below the critical volume and quasi-homogeneous ones slightly above it. The authors verify that the solution possesses the requisite single negative mode via its fluctuation eigenvalue spectrum, discuss the homogeneous-to-quasi-homogeneous crossover, provide a real-time interpretation, and apply the construction to a scalar field model as well as a (1+1)d axion-electrodynamics analogue of the Schwinger effect.

Significance. If the new bounce is confirmed to be the dominant saddle, the result would establish a geometry-driven catalysis mechanism for false-vacuum decay that is absent in infinite-volume treatments. The explicit construction of the homogeneous/quasi-homogeneous solutions, the reported crossover, and the application to both scalar and gauge models constitute concrete, falsifiable predictions that could be tested numerically or in lattice simulations. The absence of free parameters in the geometric derivation is a strength.

major comments (3)

[Abstract / fluctuation spectrum section] Abstract and the section on fluctuation analysis: the statement that 'the eigenvalue spectrum of fluctuations around the new bounce confirms the required negative mode' is presented without the explicit form of the fluctuation operator, the boundary conditions on the compact manifold, or any numerical diagonalization results. Because this negative mode is load-bearing for interpreting the solution as a decay bounce rather than a local minimum, the claim remains an assertion until the operator and spectrum are shown.
[Bounce derivation and rate comparison] Sections deriving the new bounce and comparing decay rates: the manuscript solves the Euclidean EOM on the compact manifold and obtains a distinct homogeneous solution, yet provides no direct numerical or analytic comparison of its Euclidean action against the Coleman O(D) bounce adapted to the same finite volume (or against multi-bounce configurations). Without this comparison, it is not established that the new solution is the minimal-action saddle controlling the rate below the critical volume.
[Axion electrodynamics application] Application to the Schwinger-like effect in (1+1)d axion electrodynamics: the claim of an enhanced rate relies on the same dominance assumption; an explicit action comparison or a check that no lower-action instanton exists in the compact geometry is needed before the enhancement can be asserted for this model.

minor comments (2)

[Crossover discussion] The crossover from homogeneous to quasi-homogeneous solutions is described qualitatively; a plot or table showing the action or field profile as a function of volume near the critical value would improve clarity.
[Notation] Notation for the compact manifold volume and the critical volume threshold should be introduced with a single consistent symbol and defined once in the text.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our work. We have carefully considered each point and provide detailed responses below. Where appropriate, we will revise the manuscript to address the concerns and enhance the clarity of our presentation.

read point-by-point responses

Referee: Abstract and the section on fluctuation analysis: the statement that 'the eigenvalue spectrum of fluctuations around the new bounce confirms the required negative mode' is presented without the explicit form of the fluctuation operator, the boundary conditions on the compact manifold, or any numerical diagonalization results. Because this negative mode is load-bearing for interpreting the solution as a decay bounce rather than a local minimum, the claim remains an assertion until the operator and spectrum are shown.

Authors: We appreciate the referee pointing this out. While the manuscript states that the eigenvalue spectrum confirms the negative mode, we agree that providing the explicit fluctuation operator, the boundary conditions on the compact space, and the results of the numerical diagonalization would make this more rigorous. In the revised version, we will include the derivation of the second variation operator, specify the boundary conditions (which are periodic in the compact directions), and present the numerical spectrum showing one negative eigenvalue and the rest positive, thereby confirming it is a bounce rather than a minimum. revision: yes
Referee: Sections deriving the new bounce and comparing decay rates: the manuscript solves the Euclidean EOM on the compact manifold and obtains a distinct homogeneous solution, yet provides no direct numerical or analytic comparison of its Euclidean action against the Coleman O(D) bounce adapted to the same finite volume (or against multi-bounce configurations). Without this comparison, it is not established that the new solution is the minimal-action saddle controlling the rate below the critical volume.

Authors: The new bounce is obtained by solving the Euclidean equations of motion directly on the compact manifold, leading to a homogeneous solution that is distinct from the O(D) symmetric bubble. For volumes below the critical value, this is the relevant solution. However, to address the referee's concern, we will add a direct comparison of the Euclidean actions in the revised manuscript. This will include adapting the Coleman bounce to the finite volume and comparing the actions numerically for representative parameters, as well as arguing why multi-bounce configurations have higher action and do not dominate the decay rate. revision: yes
Referee: Application to the Schwinger-like effect in (1+1)d axion electrodynamics: the claim of an enhanced rate relies on the same dominance assumption; an explicit action comparison or a check that no lower-action instanton exists in the compact geometry is needed before the enhancement can be asserted for this model.

Authors: Similar to the previous point, we will incorporate an explicit comparison of the Euclidean action for the new bounce versus other possible instantons in the compact (1+1)d axion-electrodynamics model. This will be added to the application section to substantiate the enhanced rate claim. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation solves standard Euclidean EOM on compact manifold; critical volume and rate emerge from geometry and fluctuation spectrum

full rationale

The paper begins from the standard Euclidean action for a scalar field in D compact spatial dimensions, derives the equations of motion, and numerically/analytically solves for a new homogeneous or quasi-homogeneous bounce distinct from the Coleman O(D) solution. The critical volume threshold, crossover behavior, and exponentially enhanced rate follow directly from the geometry and the properties of this solution. Confirmation that it mediates decay rests on the single negative eigenvalue in the fluctuation spectrum, which is computed from the linearized operator around the found bounce. No parameters are fitted to data and then relabeled as predictions, no self-definitional loops appear in the bounce identification, and no load-bearing uniqueness theorems or ansatze are imported via self-citation. The central steps are independent of the target claims and reduce only to the input action plus the compact boundary conditions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard Euclidean bounce formalism, the assumption that the lowest-action saddle dominates the decay rate, and the validity of analytic continuation from Euclidean to Lorentzian signature. No new particles or forces are postulated.

axioms (2)

domain assumption The decay rate is given by the exponential of minus the Euclidean action of the minimal bounce solution (standard instanton method).
Invoked throughout the abstract when stating that the new bounce mediates the decay and produces an exponentially enhanced rate.
domain assumption Analytic continuation of the Euclidean bounce yields the real-time nucleation configuration.
Used when claiming the bounce nucleates homogeneous or quasi-homogeneous field configurations in Lorentzian signature.

pith-pipeline@v0.9.0 · 5472 in / 1547 out tokens · 73272 ms · 2026-05-13T03:18:20.030172+00:00 · methodology

discussion (0)

Reference graph

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