Pith. sign in

REVIEW 2 major objections 2 minor 19 references

Supersymmetry alone does not ensure time-reversal invariance in Model A dynamics.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

2026-06-30 16:41 UTC pith:2IHX6ELT

load-bearing objection The paper builds an explicit SUSY-but-non-TRI Model A and claims FRG shows TRI emerges perturbatively with matching equilibrium flows, but the derivative expansion is the load-bearing step. the 2 major comments →

arxiv 2605.24029 v1 pith:2IHX6ELT submitted 2026-05-20 cond-mat.stat-mech cond-mat.softhep-th

Supersymmetry Without Time-Reversal Invariance in Model A: A FRG perspective

Sankarshan Sahu , Bertrand Delamotte , Adam Ran\c{c}on , Matthieu Tissier This is my paper
classification cond-mat.stat-mech cond-mat.softhep-th
keywords supersymmetrytime-reversal invarianceModel A dynamicsfunctional renormalization groupcritical dynamicsIsing modelnon-equilibrium relaxation
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.

The paper demonstrates that supersymmetry in Model A dynamics fails to guarantee relaxation to a stationary state with time-reversal invariance. An additional condition beyond supersymmetry is required to enforce this invariance. The authors construct an explicit supersymmetric model that violates time-reversal invariance yet argue that the invariance emerges effectively at large scales in a perturbative sense. Using the functional renormalization group they establish that the dynamical effective action incorporates the derivative of the equilibrium effective action and that the two share identical renormalization-group flows order by order in the derivative expansion. They further recover the probability distribution of total magnetization for the Ising model inside the Model A setting.

Core claim

Supersymmetry alone is not sufficient in Model A dynamics to ensure relaxation toward a stationary state satisfying time-reversal invariance. An additional condition on top of supersymmetry is required for TRI. A supersymmetric model violating TRI is constructed, and TRI is shown to emerge as an effective large-scale symmetry at least perturbatively. The dynamical effective action Γ[ϕ,ϕ̃] contains the derivative of the equilibrium effective action Γ^eq[ϕ] whose renormalization-group flow is identical to that of the equilibrium theory order by order in the derivative expansion.

What carries the argument

The functional renormalization group flow of the dynamical effective action Γ[ϕ,ϕ̃] and its direct relation to the derivative of the equilibrium effective action Γ^eq[ϕ].

Load-bearing premise

The functional renormalization group analysis applies order by order in the derivative expansion and the perturbative emergence of time-reversal invariance holds for the constructed model.

What would settle it

A numerical simulation of the explicitly constructed supersymmetric but TRI-violating Model A dynamics that finds persistent violation of time-reversal invariance at large scales without effective restoration.

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

If this is right

  • The renormalization-group flow of the dynamical theory matches the equilibrium flow order by order in the derivative expansion.
  • The probability distribution of the total magnetization in the Ising model is recoverable inside the Model A framework.
  • Time-reversal invariance can appear as an effective large-scale symmetry even when broken at short distances in a supersymmetric setting.

Where Pith is reading between the lines

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

  • Effective restoration of time-reversal invariance through renormalization may occur in other non-equilibrium dynamical models that possess supersymmetry.
  • The relation between dynamical and equilibrium effective actions could be used to extract equilibrium observables from non-equilibrium simulations.
  • The need for an extra condition beyond supersymmetry may generalize to other symmetry requirements in stochastic dynamics.

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

2 major / 2 minor

Summary. The paper claims that supersymmetry alone does not guarantee time-reversal invariance (TRI) in Model A dynamics; an additional condition is required. The authors explicitly construct a supersymmetric but TRI-violating model, argue that TRI emerges as an effective large-scale symmetry at least perturbatively, and use the functional renormalization group (FRG) to show that the dynamical effective action Γ[φ,φ̃] contains the derivative of the equilibrium effective action Γ^eq[φ] with identical RG flow order by order in the derivative expansion. They further recover the total magnetization probability distribution of the Ising model within the Model A framework.

Significance. If the central claims hold, the work clarifies the relationship between supersymmetry and TRI in stochastic dynamics and provides a concrete counterexample plus perturbative evidence via FRG. The explicit model construction and the demonstration of matching RG flows order-by-order in the derivative expansion are notable strengths that could influence understanding of effective symmetries in non-equilibrium systems.

major comments (2)
  1. [FRG analysis section (derivative expansion)] The load-bearing claim that the RG flow of Γ[φ,φ̃] is identical to that of Γ^eq[φ] order by order in the derivative expansion (and that this causes TRI-violating terms to become irrelevant) requires explicit verification that no relevant TRI-breaking operators are generated or persist at higher orders; the skeptic concern on this point is not resolved by the abstract alone and directly affects whether perturbative TRI emergence holds for the constructed model.
  2. [Model construction section] The explicit construction of the supersymmetric but TRI-violating model must be checked to confirm that it employs the standard stochastic supersymmetry while violating the additional TRI condition without introducing inconsistencies in the dynamics; this is central to the claim that supersymmetry alone is insufficient.
minor comments (2)
  1. [Introduction and model definition] Clarify the precise additional condition required for TRI beyond supersymmetry, including its relation to the equilibrium limit.
  2. [Ising model application] Provide more detail on how the probability distribution of total magnetization is recovered within Model A, including any explicit formulas or limits used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. We address the two major comments point by point below.

read point-by-point responses

  1. Referee: [FRG analysis section (derivative expansion)] The load-bearing claim that the RG flow of Γ[φ,φ̃] is identical to that of Γ^eq[φ] order by order in the derivative expansion (and that this causes TRI-violating terms to become irrelevant) requires explicit verification that no relevant TRI-breaking operators are generated or persist at higher orders; the skeptic concern on this point is not resolved by the abstract alone and directly affects whether perturbative TRI emergence holds for the constructed model.

    Authors: The manuscript establishes the identity between the RG flows of Γ[ϕ,ϕ̃] and Γ^eq[ϕ] order by order in the derivative expansion within the FRG framework. Because the flow preserves this structural relation at every order, any TRI-breaking operator that is absent from the equilibrium theory cannot appear as a relevant perturbation; its presence would necessarily violate the demonstrated matching. This argument is made explicitly in the FRG analysis section and supports the perturbative emergence of effective TRI. We can add a short clarifying paragraph reiterating that the order-by-order identity precludes generation of relevant breaking operators. revision: partial

  2. Referee: [Model construction section] The explicit construction of the supersymmetric but TRI-violating model must be checked to confirm that it employs the standard stochastic supersymmetry while violating the additional TRI condition without introducing inconsistencies in the dynamics; this is central to the claim that supersymmetry alone is insufficient.

    Authors: The model construction section presents an explicit supersymmetric Model A dynamics that employs the standard stochastic supersymmetry generated by the additive noise in the Langevin equation. The additional TRI condition is violated by a specific choice of the deterministic force that is compatible with supersymmetry but breaks the required relation between the drift and the equilibrium measure. The resulting stochastic process remains consistent because supersymmetry is preserved by construction and the only modification is the absence of the TRI constraint; no inconsistencies in the Fokker-Planck or path-integral formulation are introduced. This construction therefore demonstrates that supersymmetry by itself does not enforce TRI. revision: no

Circularity Check

0 steps flagged

No circularity; FRG flow identity derived from explicit model construction and derivative expansion

full rationale

The paper explicitly constructs a SUSY-but-non-TRI model, then applies FRG to show that Γ[ϕ,ϕ̃] contains dΓ^eq/dϕ and that the RG flow matches the equilibrium theory order-by-order in the derivative expansion. This identity is presented as a result of the FRG analysis rather than an input definition or fitted parameter. No self-citations are load-bearing for the central claim, no ansatz is smuggled, and no uniqueness theorem from prior work is invoked to force the outcome. The perturbative emergence of TRI is therefore an independent output of the calculation, not a renaming or self-definition. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the work relies on established supersymmetry and functional renormalization group concepts in statistical mechanics without introducing new free parameters or invented entities.

axioms (1)
  • domain assumption Functional renormalization group methods apply to the effective action in Model A dynamics.
    The paper invokes FRG to relate the dynamical and equilibrium effective actions.

pith-pipeline@v0.9.1-grok · 5705 in / 1245 out tokens · 55008 ms · 2026-06-30T16:41:59.214325+00:00 · methodology

0 comments
read the original abstract

We show that, contrary to common belief, supersymmetry alone is not sufficient in Model A dynamics to ensure relaxation toward a stationary state satisfying time-reversal invariance (TRI). An additional condition on top of supersymmetry is required for TRI, which we analyze in detail. We explicitly construct a model that is supersymmetric but violates TRI, and argue that, at least perturbatively, TRI nevertheless emerges as an effective large-scale symmetry. Using the functional renormalization group (FRG), we further show that the dynamical effective action, $\Gamma[\varphi,\tilde\varphi]$, contains the derivative of the equilibrium effective action, $\Gamma^{\mathrm{eq}}[\varphi]$, whose renormalization-group flow is identical to that of the equilibrium theory order by order in the derivative expansion. Finally, extending the same line of reasoning, we show that the probability distribution of the total magnetization in the Ising model can be recovered within the Model A framework.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages

  1. [1]

    P. C. Martin, E. D. Siggia, and H. A. Rose, Phys. Rev. A8, 423 (1973)

    work page 1973

  2. [2]

    De Dominicis, Phys

    C. De Dominicis, Phys. Rev. B18, 4913 (1978)

    work page 1978

  3. [3]

    Janssen, Z

    H.-K. Janssen, Z. Phys. B23, 377 (1976)

    work page 1976

  4. [4]

    Canet, H

    L. Canet, H. Chaté, and B. Delamotte, Journal of Physics A: Mathematical and Theoretical44, 495001 (2011)

    work page 2011

  5. [5]

    J. V . Roth, Y . Ye, S. Schlichting, and L. von Smekal, JHEP01, 118 (2025), arXiv:2403.04573 [hep-ph]

    work page arXiv 2025

  6. [6]

    Canet and H

    L. Canet and H. Chaté, Journal of Physics A: Mathematical and Theoretical40, 1937 (2007)

    work page 1937

  7. [7]

    C. Aron, G. Biroli, and L. F. Cugliandolo, Journal of Statistical Mechanics: Theory and Experiment2010, P11018 (2010)

    work page 2010

  8. [8]

    Balog, A

    I. Balog, A. Rançon, and B. Delamotte, Phys. Rev. Lett.129, 210602 (2022)

    work page 2022

  9. [9]

    Balog, B

    I. Balog, B. Delamotte, and A. Rançon, SciPost Phys.18, 119 (2025)

    work page 2025

  10. [10]

    Rançon, B

    A. Rançon, B. Delamotte, L. Šaravanja, and I. Balog, Phys. Rev. E111, 034131 (2025)

    work page 2025

  11. [11]

    F. Rose, A. Rançon, and I. Balog, Phys. Rev. E113, 054106 (2026)

    work page 2026

  12. [12]

    S. Sahu, B. Delamotte, and A. Rançon, Phys. Rev. E111, 034128 (2025). 14

    work page 2025

  13. [13]

    Sahu, Journal of Statistical Mechanics: Theory and Experiment2025, 123202 (2025)

    S. Sahu, Journal of Statistical Mechanics: Theory and Experiment2025, 123202 (2025)

    work page 2025

  14. [14]

    Sahu, Journal of Statistical Mechanics: Theory and Experiment2026, 023208 (2026)

    S. Sahu, Journal of Statistical Mechanics: Theory and Experiment2026, 023208 (2026)

    work page 2026

  15. [15]

    Eisenriegler and R

    E. Eisenriegler and R. Tomaschitz, Phys. Rev. B35, 4876 (1987)

    work page 1987

  16. [16]

    Rudnick, H

    J. Rudnick, H. Guo, and D. Jasnow, J. Stat. Phys.41, 353 (1985)

    work page 1985

  17. [17]

    Rudnick, W

    J. Rudnick, W. Lay, and D. Jasnow, Phys. Rev. E58, 2902 (1998)

    work page 1998

  18. [18]

    Canet, H

    L. Canet, H. Chaté, B. Delamotte, I. Dornic, and M. A. Muñoz, Phys. Rev. Lett.95, 100601 (2005)

    work page 2005

  19. [19]

    Canet, Journal of Statistical Mechanics: Theory and Experiment2025, 124003 (2025)

    L. Canet, Journal of Statistical Mechanics: Theory and Experiment2025, 124003 (2025)

    work page 2025