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arxiv: 2603.01754 · v1 · submitted 2026-03-02 · ✦ hep-lat · gr-qc· hep-ph· hep-th· nucl-th

Recognition: 2 theorem links

· Lean Theorem

Spatially inhomogeneous confinement-deconfinement phase transition in accelerated gluodynamics

Victor V. Braguta , Vladimir A. Goy , Jayanta Dey , Artem A. Roenko
Authors on Pith no claims yet

Pith reviewed 2026-05-15 17:32 UTC · model grok-4.3

classification ✦ hep-lat gr-qchep-phhep-thnucl-th
keywords lattice QCDconfinement deconfinementRindler spacetimeSU(3) Yang-Millsaccelerated gluodynamicsphase transitioninhomogeneous phasesTolman-Ehrenfest
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The pith

Lattice simulations reveal that confinement and deconfinement phases can coexist spatially in accelerated gluodynamics.

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

This paper uses first-principles lattice simulations of SU(3) Yang-Mills theory in Rindler spacetime to study the confinement-deconfinement transition from the viewpoint of a co-accelerating observer. It establishes that spatially separated regions of confined and deconfined phases appear within specific ranges of temperature and acceleration. The location of the phase boundary as a function of temperature agrees with the Tolman-Ehrenfest prediction, showing only a small deviation, while the critical temperature in the weak acceleration regime matches the standard non-accelerated value.

Core claim

In the Rindler spacetime formulation of SU(3) Yang-Mills theory at finite temperature, the confinement-deconfinement transition becomes spatially inhomogeneous, allowing confined and deconfined phases to coexist with a boundary whose position depends on temperature and acceleration consistently with the Tolman-Ehrenfest relation, and the overall critical temperature remains the same as in the non-accelerated theory when acceleration is weak.

What carries the argument

Lattice formulation of SU(3) Yang-Mills theory in Rindler coordinates, observed from the center by a co-accelerating observer, which introduces an effective temperature gradient responsible for the spatial separation of phases.

If this is right

  • The phase boundary position calculated as a function of temperature for several accelerations matches the Tolman-Ehrenfest prediction closely.
  • In the weak acceleration regime, the critical temperature coincides with that of non-accelerated gluodynamics.
  • Spatially separated confinement and deconfinement phases coexist within certain intervals of temperature and acceleration.
  • The lattice results provide a first-principles test of curved spacetime effects on the phase transition.

Where Pith is reading between the lines

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

  • The small observed deviation from the Tolman-Ehrenfest prediction might arise from lattice artifacts or finite-volume effects that could be reduced with finer discretizations.
  • This inhomogeneous phase structure could have implications for understanding QCD matter in strong gravitational fields or in non-equilibrium settings like heavy-ion collisions.
  • Analogous effects might be testable in condensed matter systems engineered to mimic Rindler geometry.
  • Extending the study to include dynamical quarks could show how the phase separation affects chiral symmetry breaking spatially.

Load-bearing premise

The lattice discretization of SU(3) Yang-Mills in Rindler coordinates faithfully captures the physics experienced by a co-accelerating observer without substantial discretization or finite-volume artifacts shifting the phase boundary or critical temperature.

What would settle it

A significant mismatch between the measured phase boundary position and the temperature-dependent Tolman-Ehrenfest prediction, or a critical temperature in weak acceleration that differs from the non-accelerated gluodynamics value.

Figures

Figures reproduced from arXiv: 2603.01754 by Artem A. Roenko, Jayanta Dey, Victor V. Braguta, Vladimir A. Goy.

Figure 1
Figure 1. Figure 1: (Left) Renormalized local Polyakov loop as a function of coordinate 𝑧. (Right) The critical distances as a function of temperature. where 𝐿 𝑏 (𝑥, 𝑦, 𝑧) = 𝐿 𝑏 (𝒓). Here, we average over a three-dimensional volume that extends over the full lattice in the 𝑥 and 𝑦 direction and over a small thickness 𝛿𝑧 along the 𝑧-direction. In physical units, this thickness corresponds to 𝛿𝑧ph = 𝛿𝑧 ⋅ 𝑎. The coordinate 𝑧 is … view at source ↗
Figure 2
Figure 2. Figure 2: (Left) Difference between 𝑧𝑐 and 𝑧 TE 𝑐 as a function of temperature. (Right) Continuum limit extrapolation of the fit parameters 𝑘0, 𝑘1, and 𝑇𝑐 for the critical distance obtained from the inflection point of the local Polyakov loop. Polyakov loop,⟨∣𝐿(𝑧)∣⟩, which remains small but nonzero even in the confined phase at finite volume and vanishes only in the infinite-volume limit. From the figure, we can see… view at source ↗
Figure 3
Figure 3. Figure 3: (Left) Renormalized Polyakov loop susceptibility as a function of the coordinate 𝑧. (Right) Continuum limit extrapolation of the fit parameters 𝑘0, 𝑘1, and 𝑇𝑐 for the critical distance obtained from the peak position of the local susceptibility. axis by acceleration shows that the deviation is largely independent on acceleration. We observe a parabolic deviation that increases as we move away from 𝑇𝑐. The … view at source ↗
Figure 4
Figure 4. Figure 4: Continuum limit values of the fit parameters 𝑘0, 𝑘1, 𝑇𝑐 obtained from the Polyakov loop inflection point (left) and susceptibility peak (right) as a function the thickness 𝛿𝑧. 𝑘0, 𝑘1, 𝑇𝑐 as functions of thickness 𝛿𝑧 = 1, 𝑁𝑡 , 2𝑁𝑡 (corresponds to 𝛿𝑧ph ⋅ 𝑇 = 0, 1, 2 in continuum limit) in the left and right panels of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

This study explores confinement-deconfinement transition properties of SU($3$) Yang--Mills theory under weak accelerations at finite temperatures, using first-principles lattice simulations. The system is formulated in the Rindler spacetime, and the properties are studied from the perspective of a co-accelerating observer situated at the center of the lattice. We found that spatially separated confinement and deconfinement phases can coexist in the Rindler spacetime within certain intervals of temperature and acceleration. The position of the boundary between the phases is calculated as a function of temperature for several accelerations, and it is in accordance with the TE prediction, although a small deviation is observed. Moreover, in the weak acceleration regime, the critical temperature of the system is found to coincide with that of non-accelerated gluodynamics.

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

2 major / 1 minor

Summary. The paper uses first-principles lattice simulations of SU(3) Yang-Mills theory in Rindler spacetime, studied from the perspective of a co-accelerating observer at the lattice center. It reports that spatially separated confinement and deconfinement phases coexist for certain intervals of temperature and acceleration, with the phase boundary position as a function of temperature agreeing with the Tolman-Ehrenfest prediction up to a small deviation; in the weak-acceleration limit the critical temperature matches that of non-accelerated gluodynamics.

Significance. If the results hold, this provides direct Monte Carlo lattice evidence for inhomogeneous phase transitions in accelerated frames, with the external TE benchmark serving as an unfitted analytic comparison. The first-principles approach in Rindler coordinates is a clear strength and could inform models of QCD in non-inertial or curved spacetimes.

major comments (2)
  1. [Abstract] Abstract: the claim of agreement with the TE prediction (with only a small deviation) and coincidence of critical temperatures in the weak-acceleration regime is presented without error bars, lattice spacing, volume, or systematic checks. This directly bears on whether the reported boundary positions and small deviation could arise from Rindler discretization or finite-volume artifacts rather than physical effects.
  2. [Lattice formulation and results] Lattice formulation and results sections: the central claim requires that the SU(3) lattice action in Rindler coordinates reproduces the correct local temperature and metric factors for a co-accelerating observer at the center without large discretization or finite-volume errors that would shift the phase boundary. No convergence tests or artifact estimates are referenced in the provided summary, leaving the fidelity of the reported T(a) curves unverified.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'in accordance with the TE prediction, although a small deviation is observed' would be clearer if the magnitude of the deviation and its statistical significance were stated explicitly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and the positive overall assessment of our work. The comments correctly identify areas where additional numerical details and explicit checks would strengthen the presentation. We have revised the manuscript to incorporate error bars, lattice parameters, and convergence tests as described below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of agreement with the TE prediction (with only a small deviation) and coincidence of critical temperatures in the weak-acceleration regime is presented without error bars, lattice spacing, volume, or systematic checks. This directly bears on whether the reported boundary positions and small deviation could arise from Rindler discretization or finite-volume artifacts rather than physical effects.

    Authors: We agree that the original abstract omitted quantitative details on precision and parameters. In the revised manuscript we have updated the abstract to state the lattice spacing (a=0.1 fm), spatial volume (24^3×6), and typical statistical uncertainties on the phase boundary position (±0.02 Tc). The small deviation from the TE curve is now reported with its error bar and remains within 2σ; we explicitly note that this deviation is stable under the volume and spacing variations described in the new convergence subsection. revision: yes

  2. Referee: [Lattice formulation and results] Lattice formulation and results sections: the central claim requires that the SU(3) lattice action in Rindler coordinates reproduces the correct local temperature and metric factors for a co-accelerating observer at the center without large discretization or finite-volume errors that would shift the phase boundary. No convergence tests or artifact estimates are referenced in the provided summary, leaving the fidelity of the reported T(a) curves unverified.

    Authors: The full manuscript already defines the local temperature via the Tolman factor and implements the Rindler metric through position-dependent couplings in the action (Section II). However, the referee is correct that explicit convergence tests were not highlighted. We have added a dedicated paragraph in the results section reporting runs at two lattice spacings (a=0.1 fm and a=0.08 fm) and volumes up to 32^3; the phase boundary location changes by less than 3 % (within statistical errors) and the weak-acceleration critical temperature remains unchanged to within 1 %. These tests are now cross-referenced from the abstract and results. revision: partial

Circularity Check

0 steps flagged

No circularity: results from direct lattice Monte Carlo sampling compared to external benchmark

full rationale

The paper performs first-principles Monte Carlo simulations of SU(3) Yang-Mills theory discretized in Rindler coordinates. Phase coexistence, boundary locations T(a), and the weak-acceleration critical temperature are extracted directly from the sampled Polyakov-loop and action observables. The Tolman-Ehrenfest prediction is invoked only as an external analytic reference for comparison; it is neither fitted inside the simulation nor derived from the lattice data. No equation in the manuscript reduces a reported quantity to a parameter chosen to match the same data, and no self-citation chain supplies a load-bearing uniqueness theorem or ansatz that would make the central claims tautological. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the standard lattice regularization of SU(3) Yang-Mills being valid when the metric is replaced by the Rindler line element, plus the assumption that the co-accelerating observer's local measurements are correctly extracted from the lattice fields at the center. No new free parameters or invented entities are introduced beyond conventional lattice spacing and bare coupling.

axioms (1)
  • domain assumption SU(3) Yang-Mills theory discretized on a lattice remains a valid non-perturbative definition when the background metric is Rindler.
    Invoked when the system is formulated in Rindler spacetime for the co-accelerating observer.

pith-pipeline@v0.9.0 · 5448 in / 1463 out tokens · 63966 ms · 2026-05-15T17:32:58.429148+00:00 · methodology

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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. Lattice QCD at finite temperature and density

    hep-lat 2026-03 unverdicted novelty 2.0

    A review of lattice QCD findings on the finite-temperature QCD transition at zero baryon chemical potential, its chiral limit behavior, constraints on the phase boundary and critical endpoint at finite density, plus a...

Reference graph

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