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REVIEW 3 major objections 5 minor 1 cited by

Renormalized instantons match real-time bubble profiles and decay rates from lattice simulations of vacuum decay.

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2026-07-10 23:31 UTC pith:F3VKITJB

load-bearing objection Solid 1+1D evidence that a one-parameter renormalized Coleman bounce fits stacked zero-T bubble profiles and their UV-cutoff dependence, with rates then consistent at O(1); the cosine ansatz makes the rate test a consistency check rather than fully independent proof. the 3 major comments →

arxiv 2607.06680 v1 pith:F3VKITJB submitted 2026-07-07 hep-th astro-ph.COgr-qc

Evidence for renormalized instantons in real-time simulations of vacuum decay

Emilie Hertig , Alexander C. Jenkins , Hiranya V. Peiris , Andrew Pontzen , Matthew C. Johnson This is my paper
classification hep-th astro-ph.COgr-qc
keywords false vacuum decayColeman bouncerenormalizationlattice simulationsbubble profileseffective potentialtruncated Wignercold-atom analogs
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Vacuum decay is usually described by Euclidean instanton methods that predict both the nucleation rate and the field shape of a critical bubble. Real-time lattice simulations of a relativistic scalar field produce bubbles whose ensemble-averaged profiles and rates look nothing like the bare Coleman bounce, and the mismatch grows with the ultraviolet cutoff. This paper shows that both observables are recovered once the bare potential is replaced by an effective potential whose vacuum masses are fixed analytically and whose single free parameter is fitted to the measured profiles. The same renormalized Euclidean bounce then predicts decay rates that agree with the simulations to within the expected prefactor uncertainties. The result supplies a quantitative bridge between the two formalisms and the cold-atom experiments that will soon test them.

Core claim

Ensemble-averaged bubble profiles extracted from zero-temperature lattice simulations differ from both the bare Coleman bounce and the classical critical bubble, yet are accurately reproduced by Coleman solutions computed in a renormalized effective potential whose vacuum masses are fixed by Gaussian resummation and whose single free parameter is fitted to the data; the same potential yields decay rates consistent with the simulations across the range of ultraviolet cutoffs examined.

What carries the argument

The renormalized effective potential V_eff, constructed by fixing the true- and false-vacuum masses analytically and modeling the intervening shape with a three-term cosine expansion whose only free parameter (the dimensionless energy splitting) is fitted to the stacked bubble profiles.

Load-bearing premise

The full shape of the renormalized potential between the two vacua can be captured by a three-term cosine series with only one free parameter fitted to the bubble profiles.

What would settle it

Repeat the profile extraction and rate measurement for a different bare potential (or in 2+1 dimensions) and check whether a single best-fit renormalized bounce still simultaneously reproduces both the measured profiles and the measured rates.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Euclidean instanton calculations and real-time lattice simulations become interchangeable once the effective potential is properly renormalized.
  • Cold-atom analog experiments can be designed and interpreted using the same renormalized bounce that matches the lattice data.
  • The residual O(1) rate discrepancy is attributable to the omitted one-loop fluctuation determinant, which can now be computed and tested against the same stacked profiles.
  • Multi-bubble clustering, oscillon precursors and nonzero nucleation velocities observed in simulations inherit a controlled semiclassical description.

Where Pith is reading between the lines

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

  • If the same matching holds in higher dimensions, the renormalized bounce could become the default tool for predicting gravitational-wave spectra from first-order phase transitions.
  • The observed UV-cutoff dependence of the central field value offers a direct lattice diagnostic of mass renormalization that could be checked in other nonequilibrium QFT simulations.
  • A next step is to extract the one-loop determinant from fluctuations around the stacked bubble and verify that it accounts for the remaining factor-of-a-few rate offset.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper extracts ensemble-averaged bubble profiles from zero-temperature real-time lattice simulations of false-vacuum decay for a relativistic scalar in 1+1 dimensions, using deboosting, stacking of 500 realizations, and bootstrap errors. The measured profiles (and their clear UV-cutoff dependence) differ from both the bare Coleman bounce and the critical classical bubble. The authors construct a renormalized effective potential by fixing the true- and false-vacuum masses via Gaussian resummation and parametrizing the remaining freedom with a three-term cosine expansion whose single free parameter (the dimensionless energy splitting ΔṼ) is fitted to the stacked profiles. Instanton solutions of this V_eff reproduce the profiles with substantially lower weighted χ² than bare or renormalized-classical alternatives; the same V_eff then yields Euclidean decay rates whose logarithms agree with simulation rates to O(1) across four UV cutoffs (Table I), while the bare rate is suppressed by many orders of magnitude. The authors conclude that a single renormalized Euclidean object reconciles the two formalisms.

Significance. If the correspondence holds more generally, the work supplies a quantitative bridge between Coleman instantons, real-time lattice methods, and forthcoming cold-atom analog experiments, and clarifies that classically evolved vacuum fluctuations can realize the same semiclassical process encoded by the bounce. Concrete strengths include the carefully documented profile-extraction pipeline, analytic mass renormalization that already captures the leading UV-cutoff trend, a transparent one-parameter fit, direct χ² comparison of four theoretical templates, and a multi-cutoff rate table that shows residuals remaining O(1) after a 12–14-order improvement over the bare theory. These elements make the result falsifiable and useful even if later work refines the prefactor or the potential ansatz.

major comments (3)
  1. [End Matter / Decay rates / Abstract] End Matter, Eq. (10) and surrounding text; Table I: The abstract and conclusions repeatedly call the bubble profiles and decay rates “independent observables” captured by “a single renormalized Euclidean object.” In practice ΔṼ is fitted to the stacked profiles against a renormalized Coleman template; the identical V_eff is then used to evaluate B and Γ. The rate comparison is therefore a consistency check within a one-parameter family, not an independent prediction. The language of independence and “strong evidence” should be revised to reflect this, and the residual O(1) factors should be discussed as partly expected from the hand-set prefactor D-bar ≃ 1 (Eq. 7) rather than as fully corroborating evidence.
  2. [End Matter] End Matter, Eq. (10): The three-term cosine expansion is an ansatz of convenience, not a derived effective potential. The authors note that adding one extra cosine mode leaves best-fit results essentially unchanged, but that only tests stability inside the same functional class. Because both the profile agreement and the subsequent rate predictions rest on this form, the manuscript needs either (i) a brief comparison against at least one qualitatively different parametrization (e.g., a polynomial barrier or a spline with the same mass and ΔṼ constraints) or (ii) an explicit statement that the conclusions are conditional on the cosine family adequately spanning the true V_eff. Without that, the claim that renormalization fully accounts for the discrepancy remains under-supported.
  3. [Decay rates] Decay rates section, Eq. (7) and Table I: The prefactor is set by hand to D-bar ≃ 1 and μ to the bare false-vacuum mass. Residuals Δln(Γ) are O(1) and change sign with n_cut. While the paper correctly notes that such factors are expected from the omitted one-loop determinant and from initial-state relaxation, the quantitative claim of “agreement \ldots across the parameter range” should be qualified more carefully: the decisive improvement is the removal of the 12–14-order bare discrepancy; the residual O(1) match is consistent with, but does not yet confirm, the renormalized instanton picture until D-bar is computed.
minor comments (5)
  1. [Bubble profiles / End Matter] The companion paper [29] that contains intermediate-n_cut profiles and full methodological details is listed only as “to appear.” A brief self-contained summary of the deboosting and nucleation-time algorithm (beyond the End Matter sketch) would help readers evaluate the present Letter without waiting for [29].
  2. [Figure 2] Figure 2: The weighted χ² values are reported, but the precise definition of the weights (proportional to (φ_sim−φ_FV)²/σ²) and the number of effective degrees of freedom used for the reduced χ² are given only in the text. Adding a short caption note would make the figure self-contained.
  3. [Lattice simulations] Eq. (1) and parameter choices: The values m0=1, λ=1.6, φ0=1.8 are “empirically selected” so that inverse rates match simulation timescales. A sentence on how sensitive the qualitative conclusions are to modest changes in λ or φ0 would strengthen the robustness claim.
  4. [Renormalized potential] Note [26] on the distinction between V_eff and the 1PI effective potential is important; it could be moved into the main text (one sentence) so that readers do not miss the conceptual clarification.
  5. [Table I] Table I header: “Renormalized ln(Γ)” versus “Measured ln(Γ)” is clear, but the bare value is given only in the caption; placing it in a third column or a footnote would aid quick comparison.

Circularity Check

2 steps flagged

ΔṼ fitted to profiles against renormalized Coleman template; same V_eff then used to evaluate B and Γ, so rates are consistency checks not independent predictions

specific steps
  1. fitted input called prediction [Decay rates section + End Matter (construction of V_eff, Eq. 10)]
    "treating the dimensionless energy splitting ΔṼ as the only free parameter and determining it by fitting the observed bubble profiles. ... Using the best-fit V_eff inferred from the bubble profile at each ncut (for the renormalized Coleman profile), we next solve Eq. (4) to obtain the corresponding bounce solution φ_b(x) and evaluate the exponent B ... This allows us to compute the corresponding decay rate predicted by the instanton formalism"

    ΔṼ is adjusted until the renormalized Coleman bounce matches the measured profiles; the identical fitted V_eff is then used to compute B and Γ, which are labeled 'predictions'. The rate comparison is therefore a consistency check within the one-parameter family rather than an independent first-principles test of the renormalized instanton. The abstract's claim that one object captures 'independent observables' is thereby weakened by construction.

  2. ansatz smuggled in via citation [Renormalized potential section + End Matter]
    "Following Ref. [24], we model V_eff using a three-term cosine expansion ... Although Eq. (9) fixes the curvature of V_eff near its local minima, the full shape of the renormalized potential between the true and false vacua is more challenging to calculate from first principles."

    The functional form that supplies the residual freedom (three-term cosine series) is imported from prior work by overlapping authors rather than derived; the paper itself acknowledges that the inter-vacuum shape is not fixed from first principles. Fitting the remaining coefficient to profiles then 'predicting' rates therefore inherits the ansatz, so agreement cannot uniquely establish that renormalization reconciles the formalisms outside the chosen parametrization.

full rationale

The paper's central claim is that one renormalized Euclidean object (Coleman bounce in V_eff) simultaneously accounts for two 'independent' observables: ensemble-averaged bubble profiles (incl. n_cut dependence) and decay rates. Analytic Gaussian resummation (End Matter Eq. 9) independently fixes the two vacuum masses m_eff,i as functions of the UV cutoff; this supplies genuine external content and correctly drives the observed n_cut trend in both profiles and rates. However, the residual freedom in the barrier is parametrized by a three-term cosine ansatz (Eq. 10) whose single free parameter ΔṼ is fitted directly to the stacked profiles. The identical best-fit V_eff is then inserted into the Euclidean action to obtain B and Γ (Table I), which are presented as predictions. Because the potential is constrained by one observable and tested on the other, the two are not independent; the rate agreement is a consistency check inside a one-parameter family (with D-bar set by hand to 1). Extending the cosine series by one term leaves results stable, but that only probes the chosen ansatz class. The circularity is therefore partial (score 6), not total: the mass renormalization and O(1) residual rate discrepancy remain non-circular, yet the load-bearing claim that 'a single renormalized Euclidean object captures these independent observables' reduces by construction once ΔṼ is fitted.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The central claim rests on the truncated-Wigner lattice framework, analytic Gaussian mass renormalization, a three-term cosine model for V_eff with one free parameter fitted to profiles, and the approximation that the fluctuation prefactor equals unity. These ingredients are either standard domain assumptions or explicit modeling choices introduced to close the comparison; no new physical entities are postulated.

free parameters (3)
  • ΔṼ (dimensionless energy splitting in V_eff) = best-fit values (not numerically tabulated in main text; shown to be roughly cutoff-independent and different from bare
    Sole free parameter of the three-term cosine expansion; fitted independently for each UV cutoff to the measured bubble profiles against a renormalized Coleman template.
  • bare potential parameters m0, λ, φ0 = m0=1, λ=1.6, φ0=1.8
    Fixed by hand at m0=1, λ=1.6, φ0=1.8 so that inverse decay rates fall inside simulation timescales for the chosen n_cut range.
  • fluctuation prefactor D-bar = ≃1
    Set to unity by hand following earlier work; expected to be 1+O(ħ) but not computed.
axioms (4)
  • domain assumption Truncated Wigner approximation: sampling free-field fluctuations about the false vacuum and evolving them classically captures the semiclassical nucleation process.
    Stated in Lattice simulations section and inherited from Braden et al. (2019); underpins all real-time results.
  • domain assumption Gaussian resummation of short-wavelength fluctuations yields the correct effective masses at the true and false vacua (Eq. 9).
    Taken from Braden et al. (2023) and used to fix local curvatures of V_eff.
  • ad hoc to paper A three-term cosine expansion with coefficients fixed by the two effective masses and one free energy splitting adequately models the full shape of V_eff between the vacua.
    Introduced in End Matter; authors verify that adding a fourth mode does not change results significantly, but the functional form remains an ansatz.
  • domain assumption The one-loop fluctuation determinant prefactor can be approximated as unity for the purpose of rate comparison.
    Explicitly adopted after Eq. 7; residual O(1) discrepancies are attributed to this approximation.

pith-pipeline@v1.1.0-grok45 · 15168 in / 3042 out tokens · 35713 ms · 2026-07-10T23:31:17.433930+00:00 · methodology

0 comments
read the original abstract

While vacuum decay is traditionally described by Euclidean instanton methods, lattice simulations enable real-time modeling of dynamical observables relevant to cosmology and upcoming cold-atom analog experiments. We investigate the relationship between these approaches by extracting ensemble-averaged bubble profiles from zero-temperature simulations of a relativistic scalar field. Our observed profiles differ markedly from the bare Coleman bounce and classical thermal predictions. However, we find that instanton solutions in an appropriately renormalized potential reproduce both the measured profiles and their dependence on the UV cutoff, and predict decay rates consistent with simulations across the parameter range considered. The fact that a single renormalized Euclidean object captures these independent observables provides strong evidence that renormalization accounts for the discrepancy between the two formalisms, and establishes a quantitative link between instanton predictions, lattice simulations, and forthcoming empirical tests of vacuum decay.

Figures

Figures reproduced from arXiv: 2607.06680 by Alexander C. Jenkins, Andrew Pontzen, Emilie Hertig, Hiranya V. Peiris, Matthew C. Johnson.

Figure 1
Figure 1. Figure 1: Ensemble-averaged bubble obtained from a stack of 500 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Top: Ensemble-averaged bubble profiles (solid red curves) extracted from stacks of 500 deboosted realizations with [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Effective potentials Veff [Eq. (10); colored lines] obtained by fitting the observed bubble profiles for 4 different values of the UV cutoff kUV against a renormalized Coleman template, with kNyq representing the Nyquist wavevector. These are compared to the bare potential Vbare [Eq. (1); dashed black line] [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Quantum field nucleating and Wigner functions

    hep-th 2026-07 conditional novelty 7.5

    The one-loop over-the-barrier nucleation rate in a thermal QFT is Affleck’s formula generalized to fields, not Linde’s, and still carries quantum prefactor effects even when the bounce is classically symmetric.

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