Internal color contributions to flux tube entanglement entropy

Raju Venugopalan; Rocco Amorosso; Sergey Syritsyn

REVIEW 3 major objections 4 minor 1 cited by

Internal color contributions to flux tube entanglement entropy

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read The paper argues that the dominant color contribution to flux tube entanglement entropy is $\langle F\rangle \log N_c$, with $\langle F\rangle$ the average number of full crossings of the entangling boundary, and reports SU(3) and…

desk verdict A genuine but preliminary extension of the authors' own FTE^2 conjecture; the new geometries are the interesting part, but the central evidence still leans on an unquantified vibrational subtraction. read the letter →

arxiv 2502.08737 v1 pith:WX4RCKS7 submitted 2025-02-12 hep-lat hep-phhep-thnucl-th

Rocco Amorosso , Sergey Syritsyn , Raju Venugopalan This is my paper · ORCID

classification hep-lathep-phhep-thnucl-th

keywords fluxtubeentanglemententropylatticeYang-MillstheoryRényiinternalcolorPolyakovloopsintrinsicwidthSU(2)SU(3)

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Flux tube entanglement entropy is the excess entanglement entropy of a static quark-antiquark pair in Yang-Mills theory over the vacuum value. This paper tests the conjecture that its dominant, internal color contribution equals $\langle F\rangle \log N_c$, where $N_c$ is the number of colors and $\langle F\rangle$ is the average number of times the flux tube fully crosses the boundary between the entangling region and its complement. New lattice results for SU(3) in a half-slab geometry and for SU(2) in a double-slab geometry show plateaus at $2\log 3$ and $4\log 2$, matching the predicted values for two and four crossings. The authors also compare staggered-slab geometries with and without a gap, finding that partial crossings do not count as crossings, which they interpret as evidence that FTE2 can probe the flux tube's intrinsic width. If the conjecture is right, the leading entanglement entropy of the confining flux tube is fixed purely by color counting and boundary topology.

What carries the argument

The carrying object is the identity $S_{\rm internal}=\langle F\rangle \log N_c$, with $\langle F\rangle$ the average number of complete crossings of the boundary between the entangling region $V$ and its complement. On the lattice, FTE2 is extracted from the ratio of Polyakov-loop correlators in a stack of $q$ replicas, and the identity turns a geometric counting problem into a parameter-free prediction: the $x\to-\infty$ plateau is $2\log N_c$ for the half-slab geometry and $4\log N_c$ for the double-slab geometry. The dependence of FTE2 on the transverse position of the flux tube is fitted to an error function, whose center displacement and half-width parametrize how the finite intrinsic width of the flux tube affects whether a crossing is full or partial.

What would settle it

A direct test would be to measure FTE2 at several quark-antiquark separations large enough that the known logarithmic vibrational contribution grows, subtract that contribution using an independent extraction, and check whether the residual stays at $2\log 3$ for the SU(3) half-slab geometry and $4\log 2$ for the SU(2) double-slab geometry. One could also count full boundary crossings configuration-by-configuration from the gauge fields and compare the measured $\langle F\rangle \log N_c$ with FTE2 without assuming the vibrational term is negligible.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central result is that the conjectured internal-entropy formula $S_{\rm internal}=\langle F\rangle \log N_c$ describes the measured FTE2 in two new settings: SU(3) color with two boundary crossings and SU(2) with four boundary crossings. In the SU(3) half-slab geometry the $x\to-\infty$ value of FTE2 is $2\log 3\approx 2.20$, consistent with two full crossings, and the transverse profile fits an error function with the same half-width as the earlier SU(2) measurement and a center displacement about $3/2$ as large. In the SU(2) double-slab geometry the corresponding plateau is $4\log 2$, consistent with four crossings. The gapped versus gapless staggered-slab comparison shows a substantial difference in FTE2, indicating that partial boundary intersections contribute little or nothing to the internal entropy; the authors take this as indirect evidence that only full crossings count and that FTE2 is sensitive to the intrinsic width of the flux tube. The paper presents these as preliminary results in a continuing study.

Load-bearing premise

The load-bearing premise is that the side-to-side vibration of the flux tube contributes so little to the measured excess entanglement entropy that the total can stand in for the internal color term; if that vibrational part is not actually negligible in the SU(3) or double-slab runs, the agreement with $2\log 3$ and $4\log 2$ could be coincidental.

Editorial extensions

If this is right

For any entangling geometry, the leading flux-tube entanglement is fixed by $N_c$ and by how many times the tube must cross the boundary; the detailed shape of the tube contributes only through the smaller vibrational term.
The plateaus $2\log 3$ and $4\log 2$ provide parameter-free reference numbers against which other lattice calculations or effective string models can be checked.
Partial overlaps of the flux tube with the entangling region should not be counted in $\langle F\rangle$; the effective crossing number is determined by full intersections, linking FTE2 to the tube's intrinsic width.
Effective string descriptions of confinement should include the intrinsic width of the QCD string to capture the entangling behavior seen in the staggered-slab comparison.

Reading between the lines

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

The same reasoning predicts $6\log 3$ for a double-slab SU(3) run, a cross-check that would separate the color-counting effect from any $N_c$-dependent vibrational contamination.
Introducing a curved or tilted boundary in region $V$ would test whether the crossing count in $\langle F\rangle$ is truly topological; if FTE2 depends only on the number of crossings rather than their angles, that would strengthen the identification of FTE2 with color combinatorics.
In 3+1 dimensions the relevant geometric quantity should be the number of times the flux-tube worldsheet intersects the entangling surface, so the same identity could be used to search for the string's intrinsic width where direct profile measurements are more difficult.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The new thing here is the data, not the idea: SU(3) half-slab FTE^2, a double-slab SU(2) geometry with four boundary crossings, and a staggered-slab pair that distinguishes full from partial crossings. Those are real extensions of the authors' earlier work, and the staggered-slab comparison is a nice discriminating test—it gives indirect evidence that partial crossings do not contribute to , which is a genuinely useful observation for anyone trying to understand flux tube structure.

What the paper does well is stay honest about its own status. It calls the results preliminary, and the discussion of partial versus full crossings is thoughtful. The plateau values in the half-slab and double-slab limits are consistent with 2 log 3 and 4 log 2, which is encouraging.

Now the soft spots, in proportion. The biggest one is that the comparison between the measured FTE^2 and the internal entropy prediction still runs through the assumption that S_vibrational is negligible. That was quantified in the earlier SU(2) study, but not in the SU(3) runs or in the double-slab geometry. It is a load-bearing assumption, and the paper gives no bound for it in the new ensembles. That alone makes the verdict conditional rather than confirmed. The error-function fit in Fig. 4 fixes the amplitude to 2 log N_c, so it only tests shape and offset, not the amplitude itself. The double-slab result is at one lattice spacing, and no statistical errors are reported for the plateau values. Those are all addressable, but they are real limitations.

I would not call any of this fatal. The conjecture is externally anchored by the (1+1)D result, and the new qualitative pattern—especially the difference between gapped and ungapped staggered slabs—is not something you would expect if the picture were badly wrong. Still, the paper currently reads as a proceedings contribution that presents evidence rather than a proof. If it were submitted as a full paper, I would want the statistical errors on the plateaus, a fit with free amplitude, and at least a rough estimate of the vibrational piece in the new geometries.

Who is this for? Lattice gauge theory practitioners and people working on effective string models of confinement. It is a useful data point, and the intrinsic-width claim is worth following up. I would cite it for the new geometries if I were working in that area, and I would bring it to a reading group as a good example of a conjecture being stress-tested incrementally.

Recommendation: send it to peer review, but expect heavy revision. The core idea is coherent and the new data are relevant; the presentation needs to quantify what it currently asserts.

Referee Report

3 major / 4 minor

Summary. This proceedings paper extends the flux tube entanglement entropy (FTE2) program of Refs. [1,21] to new color groups and entangling geometries. The authors conjecture that FTE2 decomposes into an internal color contribution S_internal = <F> log(N_c), where <F> is the average number of full boundary crossings, plus a smaller vibrational component. They present SU(3) half-slab results whose x->-infinity plateau approaches 2 log 3, an SU(2) double-slab result whose plateau approaches 4 log 2, and a staggered-slab gap/no-gap comparison showing a clear difference that they interpret as evidence that partial boundary crossings do not contribute like full ones. The paper concludes that the conjectured form of the internal entropy is supported for N_c=3 and F=4, and that the intrinsic width of the flux tube matters for entanglement.

Significance. If the conjectured relation S_internal = <F> log N_c holds, the dominant part of FTE2 is determined entirely by color counting and the topology of the entangling region, independent of the flux tube's transverse shape. This would be a genuinely nontrivial connection between quantum information and confinement, and the paper also proposes an interesting way to probe the intrinsic width of the flux tube. The authors are explicit that the results are preliminary, and they reproduce the expected numerical plateaus in two new settings. However, the central quantitative claim is currently supported only by comparing the total FTE2 to the internal-entropy prediction, without a direct subtraction or a quantitative bound on the vibrational contribution in the new ensembles. The paper would be strengthened by reporting statistical errors and a small continuum check for the double-slab result.

major comments (3)

[Sec. 2.2 and Sec. 3 (Figs. 3, 5, 6)] The plateau comparisons that test the central claim S_internal = <F> log N_c use the total FTE2 as a proxy for S_internal, but Eq. (8) states FTE2 = S_internal + S_vibrational. The neglect of S_vibrational is justified only by citing the earlier SU(2) study at small separations, where it was estimated to be approximately 5-10% of FTE2. No estimate or bound is given for the SU(3) half-slab ensembles or for the double-slab geometry at a sqrt(sigma0)=0.112. If the vibrational contribution is not negligible in these new runs, the apparent agreement with 2 log 3 and 4 log 2 could be coincidental. The authors should either subtract a quantitative estimate of S_vibrational (for instance, from the string model discussed in Sec. 2.2) or provide a bound showing that the contamination is small for the specific parameters used.
[Sec. 3, Fig. 4] The error-function fit in Fig. 4 is normalized to 2 log N_c and fits only the center x_c and half-width W. Consequently, it can test the shape and the offset of the profile but cannot independently validate the amplitude of the internal entropy. The wording in the Discussion that the conjecture is 'demonstrated' or 'successfully describes FTE2' overstates what this fit establishes. The independent evidence for the amplitude is the x->-infinity plateau comparison, which is subject to the vibrational-subtraction concern raised above.
[Sec. 3, Fig. 5] The double-slab result, which supports the F=4 expectation 4 log N_c, is presented at a single lattice spacing a sqrt(sigma0)=0.112 and with no statistical errors shown for the plateau values. Because this is one of only two new quantitative tests of the conjecture, the paper should report uncertainties and, ideally, a second lattice spacing to indicate discretization effects. Without these, the evidence for the F=4 case remains incomplete.

minor comments (4)

[Sec. 2.2] The statement that the vibrational entropy is 'much smaller magnitude' than the internal entropy would be more useful if accompanied by the actual values from Ref. [1] (e.g., the extracted S_vibrational and S_internal for the SU(2) half-slab), so the reader can judge the size of the neglected contribution.
[Sec. 3, Figs. 3 and 4] The axis labels in the figures appear to omit the square root: the text uses a sqrt(sigma0) and x sqrt(sigma0), while the figures show 'a σ0' and 'x σ0'. Please make the notation consistent throughout.
[Sec. 3, Fig. 4] The choice of the fit range x sqrt(sigma0) > -0.4 is not explained. A sentence on why this range was selected, and on the sensitivity of x_c and W to that choice, would strengthen the presentation.
[General] The paper does not describe the statistical error estimation method (e.g., jackknife or bootstrap) or the number of configurations used in the multilevel algorithm. Including this information, even briefly, would help the reader assess the reliability of the plateau values.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the FTE2 plateau values are measured independently and compared to the analytically motivated F log Nc prediction; the fitted error-function amplitude is not used as evidence for the amplitude.

full rationale

The central predictions of this paper, 2 log Nc for the Nc=3 half-slab geometry and 4 log Nc for the SU(2) double-slab geometry, are computed from the conjectured formula S_internal = <F> log Nc together with a geometric count of boundary crossings. They are then compared with directly measured FTE2 plateau values, which are not fitted parameters. The error-function fit in Fig. 4 does fix the amplitude to the conjectured 2 log Nc, but the paper uses that fit only to extract the offset and width; the amplitude comparison is made separately via the plateau data, so the fit does not constitute a fitted input being renamed as a prediction. The decomposition FTE2 = S_internal + S_vibrational and the assertion that S_vibrational is small are explicitly labeled as conjectures or prior results from the authors' earlier work, and the new Nc=3 and double-slab data provide fresh, independent tests that could in principle have disagreed with the conjecture. The self-citations to Refs. [1] and [21] supply the hypothesis being tested rather than forcing the measured outcome. No equation is shown to be equivalent to its own input by construction, and no fitted parameter is presented as a prediction. Therefore no circular step is exhibited.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new particles or forces. Its novel content is a numerical test of a previously conjectured formula and a new geometric probe for partial crossings. The free parameters come from the error function fits used to characterize the crossing probability profile.

free parameters (2)

x_c (error function center) = -0.27√σ0 for N_c=3; -0.19√σ0 for N_c=2
Center of the error function fit to FTE^2(x) in the half-slab geometry. Not predicted by the conjecture; interpreted as possible effect of intrinsic flux tube width.
W (error function half-width) = ≈0.3√σ0 for N_c=2 and N_c=3
Half-width of the error function fit, matched between N_c=2 and N_c=3. It describes the spread of the crossing probability.

assumptions (5)

domain assumption FTE^2 is finite, gauge-invariant, and unambiguous.
Taken from Ref. [1]; the paper relies on this definition for all measurements.
ad hoc to paper FTE^2 decomposes into internal and vibrational components.
Conjectured in Ref. [1] and used throughout; this paper tests only the internal part and assumes the partition.
ad hoc to paper Vibrational entropy is negligible (about 5-10%) compared to internal entropy.
Stated in Sec. 2.2 based on Ref. [1]; the paper identifies total FTE^2 with S_internal in the comparisons.
domain assumption Transverse fluctuations of the flux tube follow a Gaussian distribution.
Used to motivate the error function form of <F>(x) in Sec. 2.2 and the fits in Sec. 3.
domain assumption In (1+1)D Yang-Mills, FTE^2 takes the form F log N_c.
Analytical result from Ref. [21] by the same authors, used as primary motivation for Eq. (10).

how reviews work

0 comments

Cite this review

Pith. "Pith review of Internal color contributions to flux tube entanglement entropy." pith.science (2026). https://pith.science/paper/WX4RCKS7

@misc{pith2026250208737,
  author       = {Pith},
  title        = {Pith review of: Internal color contributions to flux tube entanglement entropy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WX4RCKS7}},
  note         = {Machine review of arXiv:2502.08737}
}

abstract

In recent work arXiv:2410.00112, we introduced and computed entanglement entropy of the color flux tube (FTE$^2$) between a heavy quark-antiquark pair in (2+1)D Yang-Mills theory. Our numerical results suggest that FTE$^2$ can be partitioned into a component corresponding to transverse vibrations of the flux tube and an internal color entropy. Further, motivated by analytical (1+1)D calculations, and SU(2) (2+1)D Yang-Mills numerical results, we argued that the internal entropy takes the form $\langle F\rangle\log(N_c)$, with $\langle F\rangle$ the number of times, on average, that the flux tube crossed a boundary between region $V$ and its complement. We extend here our FTE$^2$ study to consider different geometries of region $V$, varying the number of boundary crossings, and number of colors. Our preliminary results support the conjectured form of the internal entropy, albeit with noteworthy subtleties relating to the partial/full intersections of the flux tube with the region $V$.

Figures

Figures reproduced from arXiv: 2502.08737 by the authors.

**Figure 1.** Depiction of the replica geometry of a 𝐿𝑥 × 𝐿𝜏 = 6 × 3 lattice with 𝑞 = 2 replicas. The lattice has periodicity 𝐿𝑥 in the spatial direction. The lattice is 𝐿𝜏-periodic in region 𝑉¯ and 𝑞𝐿𝜏-periodic in region 𝑉. Open points on edges are wrap-around images of the sites they are connected to by dashed lines. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Left: A depiction of the “half-slab” geometry, with region 𝑉 (shaded blue) having width 𝑤 in the 𝑦 direction. The quark and antiquark sources are separated by distance 𝐿 and are located at (0, ±𝐿/2). Right: FTE2 in (2+1)D 𝑆𝑈(2) Yang-Mills theory and error function fit as a function of 𝑥 obtained by Ref. [1]. The curve is centered at 𝑥𝑐 √ 𝜎0 = −0.19 indicated by the red dashed line and has half-width 𝑊 √ 𝜎0 ≈ 0.3. Da… view at source ↗

**Figure 3.** Left: FTE2 𝑆˜ |𝑄𝑄¯ in (2+1)D 𝑆𝑈(3) Yang-Mills theory as a function of 𝑎 in the 𝑥 → −∞ limit (𝑥 √ 𝜎0 < −1.8). Here 𝑥 is the relative position of the flux tube and region 𝑉, corresponding to the half-slab geometry shown in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FTE2 in (2+1)D 𝑆𝑈(3) Yang-Mills theory as a function of 𝑥 obtained at 𝑎 √ 𝜎0 = 0.063 for 𝐿 = 12𝑎, 𝑤 = 4𝑎, and 𝑦 = 0. The green solid line is obtained by fitting the 𝑥 √ 𝜎0 > −0.4 data to an error function normalized to 2 log 𝑁𝑐 (𝑁𝑐 = 3) by varying the offset 𝑥𝑐 and the…

**Figure 5.** Figure 5: Left: “Double-slab” geometry, with region 𝑉 (shaded blue) consisting of two disconnected slabs of width 𝑤, separated by distance 𝑤gap. Right: FTE2 as a function of 𝑥 obtained for the double slab geometry at 𝑎 √ 𝜎0 = 0.112 for 𝐿 = 10𝑎, 𝑤 = 𝑤gap = 2𝑎, and 𝑦 = 0. The red …

**Figure 6.** Figure 6: (Left) Schematic of a flux tube exhibiting a full boundary crossing in the “no gap” geometry. Here the flux tube is divided into two disconnected components in 𝑉¯. (Middle) Schematic of a flux tube exhibiting a partial boundary crossing in the “gap” geometry. Here the …

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

Momentum-projected hadron entanglement from lattice-QCD replica correlators
hep-ph 2026-03 conditional novelty 6.0 of 10

The vacuum-subtracted Rényi response of a momentum-projected hadron equals 1/(1-n) times the log of a replicated source-sink correlator on the cut geometry divided by the n-th power of the ordinary correlator.

Reference graph

Works this paper leans on

32 extracted references · 6 canonical work pages · cited by 1 Pith paper

[1]

Amorosso, S

R. Amorosso, S. Syritsyn and R. Venugopalan,Entanglement entropy of a color flux tube in (2+1)D Yang-Mills theory, 2410.00112

arXiv
[2]

Kharzeev and E.M

D.E. Kharzeev and E.M. Levin,Deep inelastic scattering as a probe of entanglement,Phys. Rev. D95(2017) 114008 [1702.03489]

arXiv 2017
[3]

S.R.Beane,D.B.Kaplan,N.KlcoandM.J.Savage, EntanglementSuppressionandEmergent Symmetries of Strong Interactions,Phys. Rev. Lett.122 (2019) 102001 [1812.03138]

arXiv 2019
[4]

Kharzeev,Can gluons trace baryon number?, Phys

D. Kharzeev,Can gluons trace baryon number?, Phys. Lett. B378 (1996) 238 [nucl-th/9602027]

arXiv 1996
[5]

Berges, S

J. Berges, S. Floerchinger and R. Venugopalan,Thermal excitation spectrum from entanglement in an expanding quantum string,Phys. Lett. B778 (2018) 442 [1707.05338]

arXiv 2018
[6]

W. Gong, G. Parida, Z. Tu and R. Venugopalan,Measurement of Bell-type inequalities and quantum entanglement fromΛ-hyperon spin correlations at high energy colliders,Phys. Rev. D 106 (2022) L031501 [2107.13007]

arXiv 2022
[7]

Barata, W

J.a. Barata, W. Gong and R. Venugopalan,Realtime dynamics of hyperon spin correlations from string fragmentation in a deformed four-flavor Schwinger model, Phys. Rev. D109 (2024) 116003 [2308.13596]

arXiv 2024
[8]

Berges, M.P

J. Berges, M.P. Heller, A. Mazeliauskas and R. Venugopalan,QCD thermalization: Ab initio approaches and interdisciplinary connections, Rev. Mod. Phys.93 (2021) 035003 [2005.12299]

arXiv 2021

Show all 32 references

[9]

Davoudi, C

Z. Davoudi, C. Jarzynski, N. Mueller, G. Oruganti, C. Powers and N.Y. Halpern,Quantum Thermodynamics of Nonequilibrium Processes in Lattice Gauge Theories,Phys. Rev. Lett. 133 (2024) 250402 [2404.02965]

2024 arXiv
[10]

Bhattacharya, R

S. Bhattacharya, R. Boussarie and Y. Hatta,Spin-orbit entanglement in the Color Glass Condensate, 2404.04208

arXiv
[11]

Kharzeev,Deconfinement as an entropic self-destruction: a solution for the quarkonium suppression puzzle?, Phys

D.E. Kharzeev,Deconfinement as an entropic self-destruction: a solution for the quarkonium suppression puzzle?, Phys. Rev. D90(2014) 074007 [1409.2496]

2014 arXiv
[12]

Bombelli, R.K

L. Bombelli, R.K. Koul, J. Lee and R.D. Sorkin,A Quantum Source of Entropy for Black Holes, Phys. Rev. D34(1986) 373

1986
[13]

Srednicki,Entropy and area, Phys

M. Srednicki,Entropy and area, Phys. Rev. Lett.71(1993) 666 [hep-th/9303048]

1993 arXiv
[14]

Bulgarelli and M

A. Bulgarelli and M. Panero,Duality transformations and the entanglement entropy of gauge theories, JHEP06(2024) 041 [2404.01987]. 9 Internal color contributions to flux tube entanglement entropy Rocco Amorosso

2024 arXiv
[15]

Buividovich and M.I

P.V. Buividovich and M.I. Polikarpov,Entanglement entropy in gauge theories and the holographic principle for electric strings,Phys. Lett. B670 (2008) 141 [0806.3376]

2008 arXiv
[16]

Buividovich and M.I

P.V. Buividovich and M.I. Polikarpov,Numerical study of entanglement entropy in SU(2) lattice gauge theory,Nucl. Phys. B802 (2008) 458 [0802.4247]

2008 arXiv
[17]

E. Itou, K. Nagata, Y. Nakagawa, A. Nakamura and V.I. Zakharov,Entanglement in Four-Dimensional SU(3) Gauge Theory, PTEP2016(2016) 061B01 [1512.01334]

2016 arXiv
[18]

Rabenstein, N

A. Rabenstein, N. Bodendorfer, P. Buividovich and A. Schäfer,Lattice study of Rényi entanglement entropy in𝑆𝑈(𝑁𝑐) lattice Yang-Mills theory with𝑁𝑐= 2, 3, 4,Phys. Rev. D 100 (2019) 034504 [1812.04279]

2019 arXiv
[19]

Jokela, K

N. Jokela, K. Rummukainen, A. Salami, A. Pönni and T. Rindlisbacher,Progress in the lattice evaluation of entanglement entropy of three-dimensional Yang-Mills theories and holographic bulk reconstruction, JHEP12(2023) 137 [2304.08949]

2023 arXiv
[20]

Amorosso and S

R. Amorosso and S. Syritsyn,Entanglement Entropy due to the Presence of Static Quarks, PoSLATTICE2023(2024) 382 [2311.05825]

2024 arXiv
[21]

Amorosso, S

R. Amorosso, S. Syritsyn and R. Venugopalan,Entanglement entropy of a color flux tube in (1+1)D Yang-Mills theory, 2411.12818

arXiv
[22]

Ryu and T

S. Ryu and T. Takayanagi,Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett.96 (2006) 181602 [hep-th/0603001]

2006 arXiv
[23]

Ryu and T

S. Ryu and T. Takayanagi,Aspects of Holographic Entanglement Entropy, JHEP08(2006) 045 [hep-th/0605073]

2006 arXiv
[24]

Nishioka and T

T. Nishioka and T. Takayanagi,AdS Bubbles, Entropy and Closed String Tachyons,JHEP01 (2007) 090 [hep-th/0611035]

2007 arXiv
[25]

Klebanov, D

I.R. Klebanov, D. Kutasov and A. Murugan,Entanglement as a probe of confinement,Nucl. Phys. B796 (2008) 274 [0709.2140]

2008 arXiv
[26]

Calabrese and J.L

P. Calabrese and J.L. Cardy,Entanglement entropy and quantum field theory, J. Stat. Mech. 0406 (2004) P06002 [hep-th/0405152]

2004 arXiv
[27]

Luscher, G

M. Luscher, G. Munster and P. Weisz,How Thick Are Chromoelectric Flux Tubes?,Nucl. Phys. B180 (1981) 1

1981
[28]

Kennedy and B.J

A.D. Kennedy and B.J. Pendleton,Improved Heat Bath Method for Monte Carlo Calculations in Lattice Gauge Theories, Phys. Lett. B156(1985) 393

1985
[29]

Brown and T.J

F.R. Brown and T.J. Woch,Overrelaxed Heat Bath and Metropolis Algorithms for Accelerating Pure Gauge Monte Carlo Calculations, Phys. Rev. Lett.58(1987) 2394

1987
[30]

Luscher and P

M. Luscher and P. Weisz,Locality and exponential error reduction in numerical lattice gauge theory,JHEP09 (2001) 010 [hep-lat/0108014]. 10 Internal color contributions to flux tube entanglement entropy Rocco Amorosso

2001 arXiv
[31]

Caselle and P

M. Caselle and P. Grinza,On the intrinsic width of the chromoelectric flux tube in finite temperature LGTs,JHEP11 (2012) 174 [1207.6523]

2012 arXiv
[32]

Verzichelli, M

L. Verzichelli, M. Caselle, E. Cellini, A. Nada and D. Panfalone,Intrinsic width of the flux tube in 2+1 dimensional Yang-Mills theories, PoSLATTICE2024(2025) 403 [2501.01740]. 11

2025 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Amorosso, S

R. Amorosso, S. Syritsyn and R. Venugopalan,Entanglement entropy of a color flux tube in (2+1)D Yang-Mills theory, 2410.00112

arXiv

[2] [2]

Kharzeev and E.M

D.E. Kharzeev and E.M. Levin,Deep inelastic scattering as a probe of entanglement,Phys. Rev. D95(2017) 114008 [1702.03489]

arXiv 2017

[3] [3]

S.R.Beane,D.B.Kaplan,N.KlcoandM.J.Savage, EntanglementSuppressionandEmergent Symmetries of Strong Interactions,Phys. Rev. Lett.122 (2019) 102001 [1812.03138]

arXiv 2019

[4] [4]

Kharzeev,Can gluons trace baryon number?, Phys

D. Kharzeev,Can gluons trace baryon number?, Phys. Lett. B378 (1996) 238 [nucl-th/9602027]

arXiv 1996

[5] [5]

Berges, S

J. Berges, S. Floerchinger and R. Venugopalan,Thermal excitation spectrum from entanglement in an expanding quantum string,Phys. Lett. B778 (2018) 442 [1707.05338]

arXiv 2018

[6] [6]

W. Gong, G. Parida, Z. Tu and R. Venugopalan,Measurement of Bell-type inequalities and quantum entanglement fromΛ-hyperon spin correlations at high energy colliders,Phys. Rev. D 106 (2022) L031501 [2107.13007]

arXiv 2022

[7] [7]

Barata, W

J.a. Barata, W. Gong and R. Venugopalan,Realtime dynamics of hyperon spin correlations from string fragmentation in a deformed four-flavor Schwinger model, Phys. Rev. D109 (2024) 116003 [2308.13596]

arXiv 2024

[8] [8]

Berges, M.P

J. Berges, M.P. Heller, A. Mazeliauskas and R. Venugopalan,QCD thermalization: Ab initio approaches and interdisciplinary connections, Rev. Mod. Phys.93 (2021) 035003 [2005.12299]

arXiv 2021