Fractal phase structure of QCD under imaginary rotation

Rin Takada

REVIEW

Fractal phase structure of QCD under imaginary rotation

Rin Takada

High Energy Physics - Phenomenology · Submitted 6 Oct 2026 · 20 references

Pith's verdict: A clean boundary-condition argument extends the known T/q correspondence to a C-breaking phase structure in the bulk, with honestly acknowledged assumptions and a decisive lattice test on offer.

T0 · AI review

How this review was made: An AI referee (deepseek/deepseek-v4-flash) read the paper on October 8, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 2 major objections · 3 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv ID2610.07779 (version 1)

Pith IDS5QBTV4U, Pith's permanent record of this paper and its review

CitationRin Takada. "Fractal phase structure of QCD under imaginary rotation." arXiv:2610.07779 (2026). https://pith.science/paper/S5QBTV4U

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Takada's paper is a clean, honest extension of a known correspondence, and the new part is the one worth arguing about. The T/q thermodynamics and the p+q parity rule for imaginary angular velocity were already in the free-field and TEFT literature (Refs [1-4]), and the paper credits them. The genuinely new step is Eq. (2): the bulk at Omega_I/2pi = p/q is equivalent to nonrotating QCD at T/q with theta' = q*theta + pi(p+q+1). That mapping decides which point in the imaginary-theta plane the bulk sits at, and therefore whether that point is an RW line. At theta=0, odd/odd p,q puts the bulk at theta'=pi and C is spontaneously broken above T > q*T_RW; mixed parity puts it at theta'=0. The 2pi/3 vs 4pi/3 example works, both the algebra and the spinor sign bookkeeping. The q-fold Polyakov loop L^(q) is the right construction. The ordinary Polyakov loop is not gauge-invariant off the axis of a rotating frame, and the product of Wilson lines through x, R^{-1}x, ... closes and is invariant under R^q=1. The authors use it correctly as the bulk order parameter for the equivalent system. The "fractal" word is borrowed from earlier literature, but the content -- C-breaking exactly on the odd/odd rationals, larger denominators joining as T rises, never for irrationals -- is a genuinely new qualitative claim about thermal QCD. The irrational case, a confined bulk at any T, follows the same locality logic. Soft spots, in proportion. The locality principle is the load-bearing assumption: w2 has spatial component 2pi*r/q and is declared irrelevant for r >> xi. It is stated, not derived from QCD. I do not treat this as a red flag -- it is the standard clustering assumption behind boundary-condition reasoning in thermal field theory, and the free-field/TEFT results support it indirectly -- but it is an assumption, and the authors rightly note it needs a pure phase with finite correlation length (b42, b43) and careful limit order at the RW endpoint (b114). The regime where it matters most (T/q just above T_RW) is also the regime with the most interesting physics, so the assumption is not idle. Second, the q=1 identity and the one-loop potential behind Eq. (8) come from the author's own unpublished preprint [12]; the q>1 derivation of Eq. (3) does not use [12], so this is a moderate citation caveat, not a structural flaw. The derivation itself is not circular: for q>1 the equivalence is obtained from boundary conditions and locality, and T_RW enters as an external benchmark. The strongest element is the proposed lattice test: A = 2pi/3 vs B = 4pi/3 against nonrotating references at 3N_tau, same action and spacing, predicting equality of bulk thermodynamics without a continuum limit, with bare Im L^(3) as a renormalization-free observable. That is a parameter-free, falsifiable check of exactly the weakest assumption. This paper is for people working on imaginary rotation, the Roberge-Weiss plane, and lattice QCD in rotating frames, and it deserves a serious referee. I would send it to review, with the locality principle and the dependence on [12] as the two things to push on.

Referee report

Significance

If Eq. (3) is granted, the paper gives a striking and testable nonperturbative phase structure: imaginary rotation selects both the bulk temperature and the C-breaking sector, rationals with p and q odd form a layered set of C-broken angular velocities, and irrationals map to zero-temperature QCD. The q=3 lattice comparison is a concrete, parameter-free falsifiable prediction, and the use of the externally measured T_RW is appropriate. The paper also clearly separates the one-loop estimates from the nonperturbative equivalence. The main gap is that the central equivalence rests on an unproved locality principle and on the identification of the q-fold loop with the equivalent Polaykov loop; the proposed lattice test is exactly the right check of those assumptions.

Major objections (2)

[Bulk equivalence and order parameters, Eq. (3)] The central relation Eq. (3) rests on the locality principle: a boundary condition relating points separated by more than the correlation length is claimed not to affect local observables, so the period w_2 drops out as r\to\infty. The manuscript states this principle but does not derive it from QCD, and the regime where it is used includes the RW first-order line and the endpoint, where the required pure-phase and finite-correlation-length condition is delicate (sentences b42-b43 and b114). Because every subsequent claim, including C breaking, Eq. (6), the fractal structure, and the irrational zero-temperature limit, collapses if w_2-induced effects do not decay, this is a load-bearing assumption rather than a demonstrated consequence. I recommend that Eq. (3) be explicitly presented as conditional on locality, with a precise statement of the assumption, a discussion of the order of limits at coexistence and at the RW endpoint, and the q=3 lattice comparison framed as a test of exactly this step.
[Bulk equivalence and order parameters, Eqs. (5)-(6) and Lattice tests] The identification of L^{(q)} with the Polyakov loop of the equivalent system needs more support. H_q is a loop made of q boundary-crossing Wilson lines; in the covering space it represents q applications of the boundary condition, i.e. the cycle qv_1 = w_1 - p v_2, not the pure time cycle w_1. The paper states that because the path integral coincides locally, the distribution of L^{(q)} equals that of the equivalent Polyakov loop, but L^{(q)} is not a pointlike local observable and its winding around the spatial cylinder could distinguish it from the w_1 holonomy. Please give an argument, or a lattice demonstration within the proposed A/A_0 comparison, that the p v_2 winding does not affect the expectation value; otherwise the order-parameter predictions in Eq. (8) and the proposed test are not fully established.

Minor objections (3)

[Introduction and Discussion, Ref. [12]] The p=q=1 operator identity \hat{\rho}(\tilde{\Omega}_I+2\pi,\theta)=\hat{\rho}(\tilde{\Omega}_I,\theta+\pi), and the on-axis C-breaking window quoted in the Introduction and Discussion, are taken from the self-cited preprint [12]. Since [12] is not a published version of record and the q=1 case is used as a benchmark, the identity should either be proved in this paper or cited to a published source.
[Phase structure of the bulk] The term "fractal" is used for a set that is finite at any fixed T and grows as T increases. If that is the intended meaning, it should be defined explicitly, since the fixed-temperature set of C-breaking angular velocities is not a fractal in the usual sense.
[Lattice tests] The statement that the bulk thermodynamic quantities of A and A_0, and of B and B_0, coincide at finite lattice spacing relies on the lattice action and boundary conditions being exactly rotation-invariant on the chosen triangular lattice; this requirement is stated, but it would help to spell out which parts of the standard QCD action need modification and how the spinor rotation matrix is implemented for the B system beyond the sentence already given.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Imaginary rotation alone can break QCD's C symmetry

The reading

This paper aims to establish that the bulk of hot QCD matter rotating at an imaginary angular velocity behaves, far from the rotation axis, exactly like ordinary nonrotating QCD at a temperature divided by the denominator of the angular velocity, with a shifted imaginary chemical potential. The paper derives this from the Euclidean boundary conditions and the locality principle alone, and claims it holds nonperturbatively. It shows that when the denominator of the angular velocity is odd, the bulk sits at the Roberge-Weiss point even at zero quark chemical potential, where charge conjugation is spontaneously broken above a temperature set by the Roberge-Weiss endpoint. It also shows that the set of imaginary angular velocities that break charge conjugation has a fractal character, while irrational imaginary rotation leaves the bulk confined at all temperatures, like zero-temperature QCD.

What carries the argument

The argument rests on the Euclidean boundary condition $\tau\sim\tau+\beta$, $\varphi\sim\varphi-\tilde{\Omega}_I$ together with the locality principle: far from the rotation axis, boundary conditions relating points separated by more than the correlation length have no effect on local observables. This leaves only the pure imaginary-time period $q\beta$ in the bulk for rational $\tilde{\Omega}_I/2\pi=p/q$, fixing the bulk temperature as $T/q$. The quark boundary condition then yields the equivalent imaginary chemical potential $\theta'=q\theta+\pi(p+q+1)$, and the paper introduces the $q$-fold Polyakov loop $L^{(q)}$ as the gauge-invariant bulk order parameter that replaces the ordinary Polyakov loop away from the axis.

Extended reading notes

Core claim

The central discovery is that the boundary conditions of Euclidean QCD rotating at imaginary angular velocity $\tilde{\Omega}_I/2\pi=p/q$ force the bulk far from the rotation axis to be in the same thermal equilibrium state as nonrotating QCD at temperature $T/q$ and imaginary chemical potential $\theta'=q\theta+\pi(p+q+1)$. At zero quark chemical potential, when both $p$ and $q$ are odd, the bulk sits exactly at the Roberge-Weiss line $\theta'=\pi$, where charge conjugation is spontaneously broken for $T>qT_{\mathrm{RW}}$. The contrasting cases $\tilde{\Omega}_I=2\pi/3$ and $4\pi/3$ illustrate the claim: both bulks are equivalent to temperature $T/3$, yet only the former lies at the Roberge-Weiss point and can break $C$.

Load-bearing premise

The result assumes that locality holds in the bulk, which requires the equivalent system to be in a pure phase with finite correlation length so that distant boundary conditions do not affect local thermodynamics.

Editorial extensions

If this is right

At zero quark chemical potential, the bulk of QCD with both $p$ and $q$ odd spontaneously breaks charge conjugation for $T>qT_{\mathrm{RW}}$, giving a purely rotational route to $C$ breaking.
Irrational imaginary angular velocities confine the bulk at all temperatures on the axis, a sharp contrast with the deconfinement found at rational imaginary angular velocities.
The bulk threshold $T=qT_{\mathrm{RW}}$ is exact and coincides with singular chiral observables, making the effect testable through lattice susceptibility measurements.
Bulk thermodynamic quantities obey the parameter-free correspondence $f(T,\theta,2\pi p/q)=f(T/q,\theta',0)$, so lattice data from nonrotating QCD at rescaled temperatures directly predict rotating-bulk observables.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same boundary-condition and locality logic may apply to other symmetries of QCD, such as nonzero baryon or isospin chemical potentials, where the bulk lies at different shifted Roberge-Weiss-type points.
Since the bulk order parameter can differ from the on-axis order parameter, lattice studies of rotating QCD may need separate gauge-invariant observables for finite-radius regions.
The fractal set of $C$-breaking imaginary angular velocities may connect to rational approximations of irrational angles, so coarse temperature scans over small denominators could probe the onset of the fractal hierarchy.
The equivalence may extend to other gauge theories whose Roberge-Weiss structure differs from SU(3), yielding different denominators or symmetry-breaking patterns in the bulk.

Original abstract

We show that in hot QCD rotating at an imaginary angular velocity $\Omega_I$, the angular velocity selects not only the temperature of the bulk but whether charge conjugation $C$ is broken there. For QCD at temperature $T$ and imaginary quark chemical potential $\theta$, with $\Omega_I/2\pi=p/q$ in lowest terms, the bulk far from the rotation axis is in the same thermal equilibrium state as nonrotating QCD at temperature $T/q$ and imaginary quark chemical potential $\theta'=q\theta+\pi(p+q+1)$; this follows from the Euclidean boundary conditions and locality alone, and holds nonperturbatively. Consequently, even at zero quark chemical potential, the bulk is placed at the Roberge-Weiss (RW) point whenever $p$ and $q$ are both odd, and $C$ is spontaneously broken there for $T>qT_{\rm RW}$, with $T_{\rm RW}$ the RW endpoint temperature. The bulks at $\Omega_I=2\pi/3$ and $4\pi/3$, for example, are both at temperature $T/3$, yet only the former can break $C$. The set of imaginary angular velocities at which $C$ is broken has a fractal structure: raising $T$ adds rationals of ever larger denominator. At irrational $\Omega_I/2\pi$ the bulk corresponds to zero-temperature QCD at any $T$ and remains confined.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-07: 1 request, 5,275 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.23 · randomized assignment 0.01 · states quantitative result 0.63 · compares with prior results 0.16 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We show that in hot QCD rotating at an imaginary angular velocity $\Omega_I$, the angular velocity selects not only the temperature of the bulk but whether charge conjugation $C$ is broken there. For QCD at temperature $T$ and imaginary quark chemical potential $\theta$, with $\Omega_I/2\pi=p/q$ in lowest terms, the bulk far from the rotation axis is in the same thermal equilibrium state as nonrotating QCD at temperature $T/q$ and imaginary quark chemical potential $\theta'=q\theta+\pi(p+q+1)$; this follows from the Euclidean boundary conditions and locality alone, and holds nonperturbatively. Consequently, even at zero quark chemical potential, the bulk is placed at the Roberge-Weiss (RW) point whenever $p$ and $q$ are both odd, and $C$ is spontaneously broken there for $T>qT_{\rm RW}$, with $T_{\rm RW}$ the RW endpoint temperature. The bulks at $\Omega_I=2\pi/3$ and $4\pi/3$, for example, are both at temperature $T/3$, yet only the former can break $C$. The set of imaginary angular velocities at which $C$ is broken has a fractal structure: raising $T$ adds rationals of ever larger denominator. At irrational $\Omega_I/2\pi$ the bulk corresponds to zero-temperature QCD at any $T$ and remains confined.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show that in hot QCD rotating at an imaginary angular velocity $\Omega_I$, the angular velocity selects not only the temperature of the bulk but whether charge conjugation $C$ is broken there.	result 0.84	0.92	0.69	asserted 1.00
s1	For QCD at temperature $T$ and imaginary quark chemical potential $\theta$, with $\Omega_I/2\pi=p/q$ in lowest terms, the bulk far from the rotation axis is in the same thermal equilibrium state as nonrotating QCD at temperature $T/q$ and imaginary quark chemical potential $\theta'=q\theta+\pi(p+q+1)$; this follows from the Euclidean boundary conditions and locality alone, and holds nonperturbatively.	result 0.97	0.80	0.31	asserted 1.00
s2	Consequently, even at zero quark chemical potential, the bulk is placed at the Roberge-Weiss (RW) point whenever $p$ and $q$ are both odd, and $C$ is spontaneously broken there for $T>qT_{\rm RW}$, with $T_{\rm RW}$ the RW endpoint temperature.	result 0.81	0.77	0.28	asserted 1.00
s3	The bulks at $\Omega_I=2\pi/3$ and $4\pi/3$, for example, are both at temperature $T/3$, yet only the former can break $C$.	result 0.96	0.81	0.10	asserted 0.82
s4	The set of imaginary angular velocities at which $C$ is broken has a fractal structure: raising $T$ adds rationals of ever larger denominator.	result 0.96	0.85	0.32	asserted 1.00
s5	At irrational $\Omega_I/2\pi$ the bulk corresponds to zero-temperature QCD at any $T$ and remains confined.	result 1.00	0.81	0.11	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.96.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

Figures reproduced from arXiv:2610.07779 by the authors.

References

Works cited (20)

[12]

R. Takada, Imaginary Rotation Breaks Charge Conjuga- tion in Hot QCD, arXiv:2608.25849 (2026)

View on Pith Pith review arXiv 2026
[1]

M. N. Chernodub, Fractal thermodynamics and ninionic statistics of coherent rotational states: realization via imaginary angular rotation in imaginary time formalism, arXiv:2210.05651 (2022)

View on Pith Pith review arXiv 2022
[2]

V. E. Ambru¸ s and M. N. Chernodub, Rigidly rotating scalar fields: Between real divergence and imaginary frac- 6 talization, Phys. Rev. D108, 085016 (2023)

View on Pith 2023
[3]

T. P˘ atuleanu, A. D. Fodor, V. E. Ambru¸ s, and C. Crucean, Dirac fermions under imaginary rotation, Phys. Rev. D111, 116004 (2025)

View on Pith 2025
[4]

N. Benjamin, J. Lee, S. Pal, D. Simmons-Duffin, and Y. Xu, Angular fractals in thermal QFT, JHEP11 (2024), 134, arXiv:2405.17562 [hep-th]

View on Pith Pith review arXiv 2024
[5]

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

View on Pith 2013
[6]

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) Gluodynam- ics, JETP Lett.112, 6 (2020)

View on Pith 2020
[7]

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, 094515 (2021), arXiv:2102.05084 [hep- lat]

View on Pith Pith review arXiv 2021
[8]

M. N. Chernodub, V. A. Goy, and A. V. Molochkov, In- homogeneity of a rotating gluon plasma and the Tolman- Ehrenfest law in imaginary time: Lattice results for fast imaginary rotation, Phys. Rev. D107, 114502 (2023)

View on Pith 2023
[9]

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, 138604 (2024), arXiv:2303.03147 [hep-lat]

View on Pith Pith review arXiv 2024
[10]

S. Chen, K. Fukushima, and Y. Shimada, Perturbative Confinement in Thermal Yang-Mills Theories Induced by Imaginary Angular Velocity, Phys. Rev. Lett.129, 242002 (2022), arXiv:2207.12665 [hep-ph]

View on Pith Pith review arXiv 2022
[11]

S. Chen, K. Fukushima, and Y. Shimada, Inhomogeneous confinement and chiral symmetry breaking induced by imaginary angular velocity, Phys. Lett. B859, 139107 (2024), arXiv:2404.00965 [hep-ph]

View on Pith Pith review arXiv 2024
[13]

A. Roberge and N. Weiss, Gauge Theories With Imagi- nary Chemical Potential and the Phases of QCD, Nucl. Phys. B275, 734 (1986)

View on Pith 1986
[14]

M. D’Elia and F. Sanfilippo, The Order of the Roberge- Weiss endpoint (finite size transition) in QCD, Phys. Rev. D80, 111501 (2009)

View on Pith 2009
[15]

C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro, and F. Sanfilippo, Roberge-Weiss endpoint at the physi- cal point ofN f = 2 + 1 QCD, Phys. Rev. D93, 074504 (2016)

View on Pith 2016
[16]

Y. Aoki, S. Borsanyi, S. Durr, Z. Fodor, S. D. Katz, S. Krieg, and K. K. Szabo, The QCD transition tem- perature: results with physical masses in the continuum limit II, JHEP06(2009), 088, arXiv:0903.4155 [hep-lat]

View on Pith Pith review arXiv 2009
[17]

A. Bazavovet al.(HotQCD), Chiral crossover in QCD at zero and non-zero chemical potentials, Phys. Lett. B 795, 15 (2019), arXiv:1812.08235 [hep-lat]

View on Pith Pith review arXiv 2019
[18]

Y. Aoki, G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Sz- abo, The Order of the quantum chromodynamics transi- tion predicted by the standard model of particle physics, Nature443, 675 (2006), arXiv:hep-lat/0611014

View on Pith Pith review arXiv 2006
[19]

F. Cuteri, J. Goswami, F. Karsch, A. Lahiri, M. Neu- mann, O. Philipsen, C. Schmidt, and A. Sciarra, Toward the chiral phase transition in the Roberge-Weiss plane, Phys. Rev. D106, 014510 (2022), arXiv:2205.12707 [hep- lat]

View on Pith Pith review arXiv 2022
[20]

S. Nagy and D. N´ ogr´ adi, A Euclidean formulation of QFT incorporating finite rotations, JHEP08(2026), 030, arXiv:2509.19933

View on Pith Pith review arXiv 2026

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [12]

R. Takada, Imaginary Rotation Breaks Charge Conjuga- tion in Hot QCD, arXiv:2608.25849 (2026)

View on Pith Pith review arXiv 2026

[2] [1]

M. N. Chernodub, Fractal thermodynamics and ninionic statistics of coherent rotational states: realization via imaginary angular rotation in imaginary time formalism, arXiv:2210.05651 (2022)

View on Pith Pith review arXiv 2022

[3] [2]

V. E. Ambru¸ s and M. N. Chernodub, Rigidly rotating scalar fields: Between real divergence and imaginary frac- 6 talization, Phys. Rev. D108, 085016 (2023)

View on Pith 2023

[4] [3]

T. P˘ atuleanu, A. D. Fodor, V. E. Ambru¸ s, and C. Crucean, Dirac fermions under imaginary rotation, Phys. Rev. D111, 116004 (2025)

View on Pith 2025

[5] [4]

N. Benjamin, J. Lee, S. Pal, D. Simmons-Duffin, and Y. Xu, Angular fractals in thermal QFT, JHEP11 (2024), 134, arXiv:2405.17562 [hep-th]

View on Pith Pith review arXiv 2024

[6] [5]

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

View on Pith 2013

[7] [6]

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) Gluodynam- ics, JETP Lett.112, 6 (2020)

View on Pith 2020

[8] [7]

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, 094515 (2021), arXiv:2102.05084 [hep- lat]

View on Pith Pith review arXiv 2021

[9] [8]

M. N. Chernodub, V. A. Goy, and A. V. Molochkov, In- homogeneity of a rotating gluon plasma and the Tolman- Ehrenfest law in imaginary time: Lattice results for fast imaginary rotation, Phys. Rev. D107, 114502 (2023)

View on Pith 2023

[10] [9]

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, 138604 (2024), arXiv:2303.03147 [hep-lat]

View on Pith Pith review arXiv 2024

[11] [10]

S. Chen, K. Fukushima, and Y. Shimada, Perturbative Confinement in Thermal Yang-Mills Theories Induced by Imaginary Angular Velocity, Phys. Rev. Lett.129, 242002 (2022), arXiv:2207.12665 [hep-ph]

View on Pith Pith review arXiv 2022

[12] [11]

S. Chen, K. Fukushima, and Y. Shimada, Inhomogeneous confinement and chiral symmetry breaking induced by imaginary angular velocity, Phys. Lett. B859, 139107 (2024), arXiv:2404.00965 [hep-ph]

View on Pith Pith review arXiv 2024

[13] [13]

A. Roberge and N. Weiss, Gauge Theories With Imagi- nary Chemical Potential and the Phases of QCD, Nucl. Phys. B275, 734 (1986)

View on Pith 1986

[14] [14]

M. D’Elia and F. Sanfilippo, The Order of the Roberge- Weiss endpoint (finite size transition) in QCD, Phys. Rev. D80, 111501 (2009)

View on Pith 2009

[15] [15]

C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro, and F. Sanfilippo, Roberge-Weiss endpoint at the physi- cal point ofN f = 2 + 1 QCD, Phys. Rev. D93, 074504 (2016)

View on Pith 2016

[16] [16]

Y. Aoki, S. Borsanyi, S. Durr, Z. Fodor, S. D. Katz, S. Krieg, and K. K. Szabo, The QCD transition tem- perature: results with physical masses in the continuum limit II, JHEP06(2009), 088, arXiv:0903.4155 [hep-lat]

View on Pith Pith review arXiv 2009

[17] [17]

A. Bazavovet al.(HotQCD), Chiral crossover in QCD at zero and non-zero chemical potentials, Phys. Lett. B 795, 15 (2019), arXiv:1812.08235 [hep-lat]

View on Pith Pith review arXiv 2019

[18] [18]

Y. Aoki, G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Sz- abo, The Order of the quantum chromodynamics transi- tion predicted by the standard model of particle physics, Nature443, 675 (2006), arXiv:hep-lat/0611014

View on Pith Pith review arXiv 2006

[19] [19]

F. Cuteri, J. Goswami, F. Karsch, A. Lahiri, M. Neu- mann, O. Philipsen, C. Schmidt, and A. Sciarra, Toward the chiral phase transition in the Roberge-Weiss plane, Phys. Rev. D106, 014510 (2022), arXiv:2205.12707 [hep- lat]

View on Pith Pith review arXiv 2022

[20] [20]

S. Nagy and D. N´ ogr´ adi, A Euclidean formulation of QFT incorporating finite rotations, JHEP08(2026), 030, arXiv:2509.19933

View on Pith Pith review arXiv 2026