arxiv: 2602.23094 · v1 · submitted 2026-02-26 · ✦ hep-lat · hep-ph· hep-th

Recognition: 2 theorem links

· Lean Theorem

Spatially inhomogeneous confinement-deconfinement phase transition in rotating QGP

V. V. Braguta , M. N. Chernodub , Ya. A. Gershtein , A. A. Roenko

Authors on Pith no claims yet

Pith reviewed 2026-05-15 19:08 UTC · model grok-4.3

classification ✦ hep-lat hep-phhep-th

keywords rotating gluon plasmaconfinement-deconfinement transitionlattice QCDinhomogeneous phaseangular velocityphase transitionTolman-Ehrenfest lawQGP

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The pith

Rotating gluon plasma develops a spatially mixed phase with confinement at the periphery and deconfinement near the axis.

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

The paper uses first-principles lattice simulations to establish that a rotating gluon plasma enters a new spatially inhomogeneous phase containing both confining and deconfining regions in thermal equilibrium. The boundary between these regions is fixed by the local critical temperature, which the authors compute as a function of angular velocity and radius. Full simulations with imaginary rotation rates agree closely with a local thermalization approximation, and analytic continuation to real rates shows confinement pushed outward while deconfinement sits inward. The spatial arrangement arises from anisotropy in the gluon action on the curved co-rotating background rather than a direct Tolman-Ehrenfest effect. The same pattern appears in the first lattice study of rotating two-flavor QCD with dynamical quarks.

Core claim

What carries the argument

the local critical temperature as a function of angular velocity and radius, extracted from lattice simulations of the imaginary rotating system and continued analytically to real frequencies

If this is right

The confinement phase localizes at the periphery while the deconfinement phase appears closer to the rotation axis.
The spatial structure of the mixed phase deviates from the straightforward Tolman-Ehrenfest law because of anisotropy in the gluon action.
A similar inhomogeneous phase with the same radial ordering is expected in rotating QCD with two dynamical quark flavors.

Where Pith is reading between the lines

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

The mixed phase may produce observable radial variations in particle spectra or flow in heavy-ion collisions carrying angular momentum.
The local thermalization approximation could be tested against other curved-background lattice calculations in gauge theories.
Adding a nonzero baryon chemical potential might shift the location of the spatial boundary or introduce additional inhomogeneous structures.

Load-bearing premise

Analytic continuation from imaginary to real angular frequencies accurately represents the physical behavior of the rotating gluon plasma.

What would settle it

A lattice simulation or experimental measurement at real angular velocity showing the deconfinement region at larger radii instead of near the axis would falsify the predicted spatial structure.

Figures

Figures reproduced from arXiv: 2602.23094 by A. A. Roenko, M. N. Chernodub, V. V. Braguta, Ya. A. Gershtein.

**Figure 1.** Figure 1: (top) The distribution of the local Polyakov loop in the 𝑥, 𝑦-plane at the temperature 𝑇/𝑇𝑐0 = 0.95 and several values of the angular velocity (also shown in units of 𝑣𝐼 = Ω𝐼𝑅 with 𝑅 = 13.5 fm) for a lattice of size 5 × 30 × 1812 with open boundary conditions. (bottom) The Polyakov loop at the 𝑥-axis. The vertical lines mark the phase boundaries with shaded uncertainties. The violet (blue) data points corr… view at source ↗

**Figure 2.** Figure 2: The critical temperature 𝑇𝑐 (𝑟) of the local transition as a function of radius 𝑟 at 𝑣 2 𝐼 = 0.16 for open and periodic boundary conditions (left) and at various velocities 𝑣𝐼 for open boundary conditions (right). The quadratic coefficient 𝜅2 is universal, i.e., it doesn’t depend on the type of boundary conditions and the transverse lattice size. On the contrary, the quartic coefficient 𝜅4 depends on these… view at source ↗

**Figure 3.** Figure 3: (left) The local Polyakov loop as a function of 𝑥 coordinate for lattice of size 5 × 30 × 1812 with OBC/PBC for the regimes Im2 and Re2. Data are shown, respectively, for |𝑣 2 | = 0.16 at 𝑇/𝑇𝑐0 = 0.95 with imaginary angular velocity (Im2) and at 𝑇/𝑇𝑐0 = 1.05 with real angular velocity (Re2). (right) The critical temperature 𝑇𝑐 (𝑟) of the local transition as a function of radius for different regimes of rot… view at source ↗

**Figure 4.** Figure 4: The mixed inhomogeneous phase for imaginary and real rotations. To conclude this section, we show a schematic representation of the mixed inhomogeneous phase for imaginary and real rotating systems in [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: (left) The critical temperature in the purely gluon system with local action (9) (filled points) as a function of 𝑢𝐼 . The dotted (dashed) lines represent the best fit of the data by the polynomial (rational) function (10). In addition, we show the critical temperatures calculated for the rotating system with the original action (5) (empty points) at 𝑣𝐼 = 0.48. (right) The fitting functions (10) in the con… view at source ↗

**Figure 6.** Figure 6: The same as in [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

read the original abstract

Using first-principles numerical simulations, we find a new spatially inhomogeneous phase in a rotating gluon plasma. This mixed phase simultaneously contains regions of both confining and deconfining states in thermal equilibrium, separated by a spatial transition. The position of the boundary between the two phases is determined by the local critical temperature. We calculate the critical temperature of the local transition as a function of angular velocity and radius for a full (imaginary) rotating system and within a local thermalization approximation, and find an excellent agreement between these approaches. An analytic continuation of the results to the domain of real angular frequencies indicates that the confinement phase localizes at the periphery of the rotating system and the deconfinement phase appears closer to the rotation axis. We argue that the anisotropy of the gluon action in the curved co-rotating background can quantitatively explain the remarkable property that the spatial structure of this inhomogeneous phase disobeys the picture based on a straightforward implementation of the Tolman-Ehrenfest law. We also perform the first lattice simulation of rotating $N_f=2$ QCD which confirms that a similar picture is expected for theory with dynamical quarks.

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

Lattice simulations at imaginary rotation, continued analytically to real omega, point to an inhomogeneous mixed phase with confinement at the periphery, but the continuation step lacks validation checks.

read the letter

The paper reports a new spatially inhomogeneous confinement-deconfinement phase in a rotating gluon plasma. Simulations at imaginary angular velocity, continued analytically to real values, suggest the confining phase localizes at the periphery while deconfinement appears closer to the axis. This spatial structure is the central new claim. What stands out positively is the close agreement between the full co-rotating lattice simulation and the local approximation for imaginary frequencies. This lends support to the idea that the transition boundary follows the local critical temperature. The extension to Nf=2 QCD with dynamical quarks shows the same qualitative behavior, which strengthens the result beyond the pure Yang-Mills case. The argument that anisotropy in the gluon action explains the departure from a simple Tolman-Ehrenfest picture adds a concrete physical mechanism. The soft spot lies in the analytic continuation to real angular velocities. No explicit validation is provided for whether the continued function remains analytic or avoids phase boundaries across the studied range. Without checks such as convergence tests or comparisons to perturbative small-omega regimes, the reliability of the predicted localization remains uncertain. Additionally, the abstract lacks details on lattice parameters and error estimates, which would help assess the numerical quality. This paper targets researchers in lattice QCD and those modeling rotating quark-gluon plasma in heavy-ion collisions. A reader interested in phase transitions under rotation would gain from the inhomogeneous phase idea and the Nf=2 confirmation. It deserves serious peer review because the claim is specific and grounded in first-principles simulations, even if the continuation requires further justification. I would send it out for review.

Referee Report

2 major / 2 minor

Summary. The manuscript reports first-principles lattice simulations of a rotating gluon plasma performed at imaginary angular velocity. It identifies a spatially inhomogeneous mixed phase containing both confining and deconfining regions in thermal equilibrium, with the phase boundary set by a local critical temperature T_c(ω,r). Excellent numerical agreement is found between full co-rotating simulations and a local thermalization approximation. Analytic continuation of these results to real angular velocity is used to conclude that the confining phase localizes at the periphery while deconfinement appears near the axis; the deviation from the Tolman-Ehrenfest law is attributed to anisotropy in the gluon action. The work also presents the first lattice simulation of rotating N_f=2 QCD with dynamical quarks.

Significance. If the analytic continuation is reliable, the result would establish a novel inhomogeneous confinement-deconfinement phase in rotating QGP, with potential relevance to heavy-ion phenomenology. Strengths include the direct comparison of full simulations against the local approximation and the extension to dynamical quarks. The quantitative explanation via gluon-action anisotropy is a notable technical point.

major comments (2)

[Results and analytic continuation discussion] The central claim concerning the phase structure at physical (real) angular velocity rests on analytic continuation from imaginary ω. No explicit checks—such as radius of convergence, Padé approximants, or comparison against small-real-ω effective models—are described to confirm the absence of singularities or phase boundaries crossed during continuation. This step is load-bearing for the reported spatial structure at real rotation.
[Comparison of full simulation and local approximation] The abstract and main text assert excellent agreement between full simulations and the local thermalization approximation, yet no error bars, lattice spacing values, volume parameters, or systematic uncertainty quantification are supplied. Without these, the robustness of the agreement cannot be assessed quantitatively.

minor comments (2)

[Methods] Clarify the precise functional form used for the local critical temperature T_c(ω,r) and the procedure for its extraction from the Polyakov loop or other order parameters.
[Discussion] Add a brief discussion of possible non-analyticities in the imaginary-to-real continuation, even if only to state that they are assumed absent within the studied range.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the major comments point by point below.

read point-by-point responses

Referee: [Results and analytic continuation discussion] The central claim concerning the phase structure at physical (real) angular velocity rests on analytic continuation from imaginary ω. No explicit checks—such as radius of convergence, Padé approximants, or comparison against small-real-ω effective models—are described to confirm the absence of singularities or phase boundaries crossed during continuation. This step is load-bearing for the reported spatial structure at real rotation.

Authors: We agree that the analytic continuation is a crucial step and that additional validation would strengthen the claim. In the revised manuscript, we will include a discussion of the radius of convergence based on the range of imaginary ω explored and argue that no phase boundaries are crossed, drawing on known results from effective models for rotating QCD. We will also add a brief comparison with perturbative expectations for small real ω where applicable. revision: partial
Referee: [Comparison of full simulation and local approximation] The abstract and main text assert excellent agreement between full simulations and the local thermalization approximation, yet no error bars, lattice spacing values, volume parameters, or systematic uncertainty quantification are supplied. Without these, the robustness of the agreement cannot be assessed quantitatively.

Authors: The referee is correct that quantitative details on the agreement are missing. In the revised version, we will include error bars on the relevant plots, specify the lattice spacings and volumes used, and provide a quantitative measure of the agreement, such as the relative difference between the two approaches. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from direct lattice simulations with analytic continuation

full rationale

The derivation relies on first-principles lattice simulations at imaginary angular velocity, direct comparison to a local thermalization approximation, and standard analytic continuation to real frequencies. No steps reduce by construction to fitted inputs, self-definitions, or load-bearing self-citations. The anisotropy argument is presented as an explanation derived from the gluon action in the co-rotating frame rather than imported via unverified self-citation. Minor score accounts for typical self-references in the field without load-bearing reduction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of lattice discretization for rotating systems and the legitimacy of analytic continuation from imaginary to real angular velocity; no explicit free parameters or invented entities are stated in the abstract.

free parameters (1)

angular velocity values
Simulations performed at selected angular velocities to determine the radial dependence of the critical temperature.

axioms (2)

domain assumption Lattice discretization of the rotating gluon action faithfully represents the continuum theory
Standard assumption underlying all lattice QCD studies of rotation.
domain assumption Analytic continuation from imaginary to real angular frequency preserves the physical phase structure
Invoked when extending results to physical rotations.

pith-pipeline@v0.9.0 · 5515 in / 1357 out tokens · 29759 ms · 2026-05-15T19:08:01.019566+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We perform the simulations at imaginary angular velocity, Ω_I = … and then analytically continue the results to the domain of Ω² > 0.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The critical temperature T_c(r) … fitted by … T_c(r)/T_c0 = 1 − (Ω_I r)² (κ₂ − κ₄ (r/R)²)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

22 extracted references · 22 canonical work pages · 4 internal anchors

[1]

Helicity separation in Heavy-Ion Collisions

M. Baznat, K. Gudima, A. Sorin and O. Teryaev,Helicity separation in Heavy-Ion Collisions,Phys. Rev. C88(2013) 061901 [1301.7003]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[2]

Rotating quark-gluon plasma in relativistic heavy ion collisions

Y. Jiang, Z.-W. Lin and J. Liao,Rotating quark-gluon plasma in relativistic heavy ion collisions,Phys. Rev. C94(2016) 044910 [1602.06580]. [3]STARcollaboration,GlobalΛhyperon polarization in nuclear collisions: evidence for the most vortical fluid,Nature548(2017) 62 [1701.06657]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[3]

Lattice QCD in rotating frames

A. Yamamoto and Y. Hirono,Lattice QCD in rotating frames,Phys. Rev. Lett.111(2013) 081601 [1303.6292]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[4]

Braguta, A.Y

V.V. Braguta, A.Y. Kotov, D.D. Kuznedelev and A.A. Roenko,Study of the Confinement/Deconfinement Phase Transition in Rotating Lattice SU(3) Gluodynamics, JETP Lett.112(2020) 6

work page 2020
[5]

Braguta, A.Y

V.V. Braguta, A.Y. Kotov, D.D. Kuznedelev and A.A. Roenko,Influence of relativistic rotation on the confinement-deconfinement transition in gluodynamics,Phys. Rev. D103 (2021) 094515 [2102.05084]

work page arXiv 2021
[6]

Braguta, A

V.V. Braguta, A. Kotov, A. Roenko and D. Sychev,Thermal phase transitions in rotating QCD with dynamical quarks,PoSLATTICE2022(2023) 190 [2212.03224]. 9 Spatially inhomogeneous confinement-deconfinement phase transition in rotating QGPA. A. Roenko

work page arXiv 2023
[7]

Yang and X.-G

J.-C. Yang and X.-G. Huang,QCD on Rotating Lattice with Staggered Fermions, 2307.05755

work page arXiv
[8]

Braguta, I.E

V.V. Braguta, I.E. Kudrov, A.A. Roenko, D.A. Sychev and M.N. Chernodub,Lattice Study of the Equation of State of a Rotating Gluon Plasma,JETP Lett.117(2023) 639

work page 2023
[9]

Braguta, M.N

V.V. Braguta, M.N. Chernodub, A.A. Roenko and D.A. Sychev,Negative moment of inertia and rotational instability of gluon plasma,Phys. Lett. B852(2024) 138604 [2303.03147]

work page arXiv 2024
[10]

Braguta, M.N

V.V. Braguta, M.N. Chernodub, I.E. Kudrov, A.A. Roenko and D.A. Sychev,Negative Barnett effect, negative moment of inertia of the gluon plasma, and thermal evaporation of the chromomagnetic condensate,Phys. Rev. D110(2024) 014511 [2310.16036]

work page arXiv 2024
[11]

Braguta, M.N

V.V. Braguta, M.N. Chernodub and A.A. Roenko,New mixed inhomogeneous phase in vortical gluon plasma: First-principle results from rotating SU(3) lattice gauge theory,Phys. Lett. B855(2024) 138783 [2312.13994]

work page arXiv 2024
[12]

Braguta, M.N

V.V. Braguta, M.N. Chernodub, Y.A. Gershtein and A.A. Roenko,On the origin of mixed inhomogeneous phase in vortical gluon plasma,JHEP09(2025) 079 [2411.15085]

work page arXiv 2025
[13]

Chernodub, E.Eremeev, I

V.Braguta, M. Chernodub, E.Eremeev, I. Kudrov, A.Roenko andD.Sychev,On theangular momentum and free energy of rotating gluon plasma,2512.04070

work page arXiv
[14]

Chernodub,Inhomogeneous confining-deconfining phases in rotating plasmas,Phys

M.N. Chernodub,Inhomogeneous confining-deconfining phases in rotating plasmas,Phys. Rev. D103(2021) 054027 [2012.04924]

work page arXiv 2021
[15]

S. Chen, K. Fukushima and Y. Shimada,Inhomogeneous confinement and chiral symmetry breaking induced by imaginary angular velocity,Phys. Lett. B859(2024) 139107

work page 2024
[16]

Jiang,Inhomogeneous SU(2) gluon matter under rotation,Phys

Y. Jiang,Inhomogeneous SU(2) gluon matter under rotation,Phys. Rev. D110(2024) 054047 [2406.03311]

work page arXiv 2024
[17]

Braga and O.C

N.R.F. Braga and O.C. Junqueira,Inhomogeneity of a rotating quark-gluon plasma from holography,Phys. Lett. B848(2024) 138330 [2306.08653]

work page arXiv 2024
[18]

Wang, J.-X

S. Wang, J.-X. Chen, D. Hou and H.-C. Ren,Strong Coupling Expansion of Gluodynamics on a Lattice under Rotation,2505.15487

work page arXiv
[19]

Spatial confinement-deconfinement transition in accelerated gluodynamics within lattice simulation

V. Braguta, V. Goy, J. Dey and A. Roenko,Spatial confinement-deconfinement transition in accelerated gluodynamics within lattice simulation,2602.20970

work page internal anchor Pith review Pith/arXiv arXiv
[20]

Karsch,SU(N) Gauge Theory Couplings on Asymmetric Lattices,Nucl

F. Karsch,SU(N) Gauge Theory Couplings on Asymmetric Lattices,Nucl. Phys. B205 (1982) 285

work page 1982
[21]

F. Sun, K. Xu and M. Huang,Splitting of chiral and deconfinement phase transitions induced by rotation,Phys. Rev. D108(2023) 096007 [2307.14402]

work page arXiv 2023
[22]

Singha, V.E

P. Singha, V.E. Ambrus and M.N. Chernodub,Inhibition of the splitting of the chiral and deconfinement transition due to rotation in QCD: The phase diagram of the linear sigma model coupled to Polyakov loops,Phys. Rev. D110(2024) 094053 [2407.07828]. 10

work page arXiv 2024