Charged Black Hole with String Cloud Deformation: Entanglement and Chaos

Arpit Maurya; Himanshu Parihar; Sanjay Pant; Shagun Kaushal

REVIEW 4 major objections 4 minor 58 references

Charged Black Hole with String Cloud Deformation: Entanglement and Chaos

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that charge and string-cloud backreaction in a holographic plasma raise entanglement entropy and entanglement-wedge cross-section, lower mutual information and butterfly velocity, and make two-sided correlations more…

desk verdict A systematic parameter scan whose new charge-dependence claims are undermined by a likely RT formula error and inconsistent temperature normalizations. read the letter →

arxiv 2507.10455 v1 pith:2SILWO7P submitted 2025-07-14 hep-th

Shagun Kaushal , Arpit Maurya , Sanjay Pant , Himanshu Parihar This is my paper

classification hep-th PACS 04.70.-s11.25.Tq03.65.Ud

keywords holographicentanglemententropywedgecross-sectionbutterflyvelocitythermomutualinformationstringcloudchargedAdSblackholeshockwavescramblingS/CFTcorrespondence

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

This paper asks how electric charge and a uniform cloud of strings—the holographic stand-in for heavy static fundamental quarks—reshape entanglement and chaos in a strongly coupled plasma. Working within the AdS/CFT correspondence, it computes five quantum-information observables in a charged AdS black hole deformed by string-cloud backreaction: entanglement entropy, mutual information, entanglement-wedge cross-section, butterfly velocity, and thermo mutual information. It finds that entanglement entropy and the entanglement-wedge cross-section grow monotonically with both charge and backreaction, while mutual information grows with backreaction but shrinks with charge. The butterfly velocity decreases with both parameters, and thermo mutual information across the two-sided black hole is destroyed by a weaker shock when charge is present. The upshot is a coherent picture in which backreaction enriches correlations, while charge enriches some measures, screens others, and makes the two-sided correlations more fragile under perturbation.

What carries the argument

The load-bearing object is the deformed blackening function $f(z) = 1 - \rho (z/z_h)^{d-1} + (\rho-\sigma-1)(z/z_h)^d + \sigma (z/z_h)^{2d-2}$, with $\rho$ the dimensionless string-cloud density and $\sigma$ the dimensionless charge parameter; every extremal-surface area and near-horizon shockwave quantity is computed from this function. On top of it, the machinery consists of the Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi prescriptions for holographic entanglement entropy, the entanglement-wedge cross-section formula, and the shockwave shift function $\alpha$ whose spatial decay profile gives $M = \lambda_L/v_B$ and the closed-form butterfly velocity. The same shockwave parameter, recast through the extremal-surface turning point $z_0$, controls the destruction of thermo mutual information.

What would settle it

A direct numerical scan of the thermo-mutual-information integral in Eq. (6.2) at fixed temperature and backreaction, varying the charge parameter $\sigma$, would settle whether the critical width $l_c$ increases or decreases with charge, since the paper's prose and figure caption disagree on that point. Separately, computing the butterfly velocity by pole-skipping or by an independent OTOC calculation in the same background and comparing with $v_B^2 = (d-\rho-(d-2)\sigma)/(2(d-1))$ would test the shockwave derivation directly.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the dimensionless charge parameter $\sigma$ and the string-cloud backreaction parameter $\rho$ together modify the dual field theory in a coherent but two-faced way. Holographic entanglement entropy and the entanglement-wedge cross-section increase monotonically with both parameters, indicating additional bulk degrees of freedom that enrich boundary correlations; mutual information also rises with $\rho$ but falls with $\sigma$. The butterfly velocity obeys $v_B^2 = (d-\rho-(d-2)\sigma)/(2(d-1))$, so it decreases with both charge and backreaction and vanishes at a critical $\rho$ that shrinks as charge grows. In the two-sided setup, thermo mutual information appears above a critical strip width and, under a shockwave perturbation, is completely disrupted beyond a critical shock strength that decreases with increasing charge. The paper interprets this as charge both enriching the entanglement structure and acting as an effective barrier to operator growth and a catalyst for shock-induced scrambling.

Load-bearing premise

The entire calculation assumes that the averaged string-cloud stress tensor, leading to the metric in Eq. (2.19), is the correct holographic dual of a large-$N$ field theory at finite temperature and chemical potential with a uniform heavy-quark cloud; if that averaging misses real string dynamics, every observable computed here would change.

Editorial extensions

If this is right

At fixed strip width, entanglement entropy and the entanglement-wedge cross-section are larger in the charged, backreacted background than in the uncharged AdS-Schwarzschild baseline, so mixed-state correlations are stronger.
Reality of $v_B$ imposes $d \geq \rho + (d-2)\sigma$; at the boundary of this region the butterfly velocity vanishes, so a sufficiently charged or dense-string plasma would show no spatial spread of chaos.
Thermo mutual information across the two boundaries survives only below a critical shock strength, and that strength is smaller for larger charge, meaning charged plasmas lose inter-boundary correlations under weaker perturbations.
The bound $E_W \geq I/2$ holds across the scanned parameter range, supporting the claim that the entanglement-wedge cross-section sees correlations that mutual information misses.
Entanglement velocity stays below butterfly velocity and approaches the same $d/(2(d-1))$ upper bound, so the standard holographic ordering $v_E \leq v_B$ survives the deformation.

Reading between the lines

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

If the averaged string-cloud stress tensor is the correct effective description, the monotonic rise of entanglement entropy and EWCS with $\sigma$ suggests charge acts like an effective increase in the number of active degrees of freedom; one could test this by comparing the entropy density $s \sim z_h^{-(d-1)}$ with the free-energy density from the same metric.
The closed form for $v_B$ is a parameter-free prediction that could be checked independently by pole-skipping or by a direct OTOC computation in this background; a mismatch would localize the error to the shockwave matching rather than to the entanglement integrals.
The same shockwave construction could be applied to holographic entanglement negativity or complexity; the pattern found here would predict that charge accelerates their late-time growth even while lowering $v_B$.
One could combine the temperature-positivity bound $d \geq (\rho - 2\sigma)/(1-\sigma)$ with $v_B^2 \geq 0$ to map out the full physical region of the $(\rho, \sigma)$ plane, which the paper does not do explicitly.

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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

Dear [Colleague],

This is a workmanlike holography paper that runs a standard menu of observables—EE, MI, EWCS, butterfly velocity, TMI and shockwave disruption—on the charged string-cloud AdS black hole from Ref. [48]. The zero-charge limits match earlier work [44,45], and the charge dependence is genuinely new. The computations are standard applications, no new formalism, and the paper is clearly organized. That's the good news.

The soft spots are significant. First, the RT entropy formula in Eq. (3.2) looks wrong: it has sqrt(f(z)) in the numerator, whereas the correct integrand for this metric is 1/(sqrt(f(z)) sqrt(1 - (z/z_t)^{2d-2})). The same form appears in Eqs. (4.4) and (6.2), so all entropy, MI, and TMI numerics are suspect. If it's a typo, the authors must say so; if not, the numerical results are invalid. Second, the temperature normalization is inconsistent. T = (d - ρ - (d-2)σ)/(4π z_h), so varying ρ or σ at fixed z_h changes T. Fig. 2 (left) and Fig. 8 fix T=1; Fig. 9 fixes z_h=1; Figs. 3, 4, and 7 don't state which. The plotted monotonic trends could be temperature artifacts. Third, the critical width l_c for TMI is described in contradictory ways: Fig. 8's caption says it increases with σ, while the text in Sections 6 and 8 says it decreases. Since the sign of dl_c/dσ determines whether charge suppresses or enhances TMI, this is not a minor typo.

The butterfly velocity analysis is analytic and likely fine, as is the shock parameter relation. But the central numerical claims about charge dependence are not established until these issues are addressed.

Who is this for? People working on holographic entanglement in backreacted geometries might use it once corrected. It deserves a serious referee because the topic is legitimate and the zero-charge checks suggest the authors are competent. I'd recommend major revision: correct the formula, redo all comparisons at fixed T, and fix the l_c contradiction.

In current form, I wouldn't cite it or use its numbers, but I'd engage with a revised version.

Best

Referee Report

4 major / 4 minor

Summary. The paper studies holographic observables in a charged AdS black hole deformed by a homogeneous string cloud, dual to a large-Nc strongly coupled field theory at finite temperature and chemical potential with a heavy-quark cloud. It computes holographic entanglement entropy (HEE), mutual information (MI), entanglement wedge cross-section (EWCS), butterfly velocity, and thermo mutual information (TMI) with and without shockwave perturbations. The claimed results are that HEE and EWCS increase monotonically with both charge and backreaction, MI and TMI decrease with charge while backreaction strengthens correlations, butterfly velocity decreases with both parameters, and the critical shock strength for TMI disruption decreases with charge.

Significance. If the reported results are correct, the paper provides a systematic characterization of how electric charge and string-cloud backreaction jointly shape entanglement structure and chaos in a strongly coupled holographic plasma. The analytic butterfly-velocity formula in Eq. (5.16) and its consistency checks against known AdS-Schwarzschild and string-cloud limits are useful. The paper also verifies the inequality EW >= I/2 numerically. However, the central numerical claims rest on an inverted RT entropy integrand and on comparisons that do not consistently fix the thermodynamic ensemble, so the significance of the detailed trends is not established by the present manuscript.

major comments (4)

[§3, Eq. (3.2)] The holographic entanglement entropy formula has the factor sqrt(1 - (z/zt)^(2d-2)) in the numerator, whereas the standard derivation from the induced metric on the extremal surface places this factor in the denominator: S = (L^(d-2) R^(d-1)/(2G)) ∫ dz / [z^(d-1) sqrt(f(z)) sqrt(1 - (z/zt)^(2d-2))]. Equation (3.3) for the strip width, which is consistent with the standard x'(z) relation, has the factor in the denominator. Thus Eq. (3.2) is internally inconsistent with Eq. (3.3), and every numerical result derived from it — including Eqs. (4.4) and (6.2) and the plots in Figs. 2, 3, 4, 8, and 9 — is suspect until recomputed with the corrected integrand.
[§4, Fig. 3] The text says the subsystem widths are kept fixed by fixing the turning points zt(D)=0.01, zt(l)=0.4, and zt(2l+D)=0.7, but Eq. (3.3) shows that the width l depends on f(z), which depends on both rho and sigma. Fixing zt therefore does not fix l or D as rho and sigma vary. The reported comparison that MI decreases with sigma at fixed rho may be an artifact of comparing different boundary interval sizes rather than a genuine charge effect, and the same issue affects the EWCS comparison in Fig. 4.
[§6, Fig. 8 and §8] The manuscript contradicts itself on how the critical width lc depends on charge. Section 6 states 'As the sigma increases, the critical width lc shifts to the smaller values,' while the Fig. 8 caption states 'lc, which increases with sigma,' and Section 8 repeats that increasing sigma 'reduces the critical width lc.' These statements are mutually exclusive; the direction of the charge effect on the TMI threshold must be settled by a corrected numerical computation and stated consistently.
[§7, Fig. 9] The shock-wave TMI and Sreg computations are performed at fixed z_h = 1, not at fixed temperature. Since T = (d - rho - (d-2) sigma)/(4 pi z_h) from Eq. (2.22), varying sigma at fixed z_h changes T across the plotted curves. The claim that increasing charge decreases the critical shock strength, and the related claim that charge enhances scrambling, may therefore be a temperature artifact. Figures 3, 4, and 7 also do not state which quantity (T or z_h) is held fixed, so the reported monotonic trends in rho and sigma are not defined on a common thermodynamic ensemble.

minor comments (4)

[§5, Eq. (5.10)] The quantity A(zh) appears in Eq. (5.10) and in the definition of M^2 in Eq. (5.11) but is never defined in the text; please define it explicitly or remove it by writing M^2 directly in terms of g_xx and its derivative.
[§3, Fig. 2 and Fig. 8] The horizontal axis in Figs. 2 (left) and 8 is labeled 'Tl' while the captions describe the quantity as the width l at fixed T=1; the label should be l (or T l should be clearly explained).
[§8] The summary states that 'MI vanishes beyond a critical value of rho,' but the numerical section and Fig. 3 do not demonstrate a vanishing MI; the curves terminate at parameter bounds rather than at I=0. Please either show the vanishing explicitly or rephrase the summary.
[§2] There are typographical issues in section 2, including missing spaces in 'finitetemperatureandfinitechemicalpotential' and inconsistent notation for the string-cloud energy-momentum tensor components; a careful proofread is needed.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the entanglement and chaos results are obtained by applying standard holographic formulas to an externally derived metric, with self-citations used only as consistency checks.

full rationale

The derivation chain is self-contained with respect to the claimed outputs. The black hole metric (2.19) is imported from Ref. [48], an external and independently derived solution, and every observable—HEE (Eq. 3.2), HMI (Eq. 4.4), EWCS (Eq. 4.6), v_B (Eq. 5.16), and TMI (Eq. 6.2)—is obtained by inserting this metric into standard holographic prescriptions (RT/HRT area, shockwave matching). No parameter is fitted to the target observables, and no observable is defined so as to enforce the reported monotonic trends; the plots are numerical evaluations of the resulting integrals. The paper's self-citations [44], [45], and [46] appear only as zero-charge/backreaction consistency checks and as methodological references (for example, 'the previously established expression for the butterfly velocity in the holographic string cloud background, as reported in [45]'), and none supplies a premise needed to obtain the charge-dependent claims. I therefore find no circular step. A separate, non-circularity concern is that some plots hold z_h = 1 while others hold T = 1 (Figs. 8 versus 9), and the text disagrees about whether l_c increases or decreases with sigma (Fig. 8 caption and Section 8 versus Section 6); those issues affect the robustness of the physical interpretation, not the logical self-containedness of the computation.

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

The paper introduces no new free parameters or entities; it uses the parameters rho and sigma from the existing background. The axioms are standard holographic tools and the background metric from prior work.

assumptions (5)

domain assumption AdS/CFT correspondence holds for this background
The paper uses the duality to interpret bulk computations as boundary observables, introduced in Section 1.
domain assumption Ryu-Takayanagi formula for entanglement entropy (and HRT extension)
The RT prescription is used in Eq. (3.2) to compute entanglement entropy, and the HRT extension is used for TMI in Section 6.
domain assumption Entanglement wedge cross-section is dual to entanglement of purification
The EWCS is computed using the conjectured dual in Section 4, following Refs. [10,11].
domain assumption Shockwave geometry and exponential OTOC growth characterize chaos
The paper uses the shockwave method in Section 5 to derive butterfly velocity and Lyapunov exponent, following standard holographic chaos literature.
ad hoc to paper The metric in Eq. (2.19) is a valid solution of the Einstein-Maxwell equations with string cloud
This metric is taken from Ref. [48] and is assumed to be the correct dual background. It is not derived in this paper.

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Pith. "Pith review of Charged Black Hole with String Cloud Deformation: Entanglement and Chaos." pith.science (2026). https://pith.science/paper/2SILWO7P

@misc{pith2026250710455,
  author       = {Pith},
  title        = {Pith review of: Charged Black Hole with String Cloud Deformation: Entanglement and Chaos},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2SILWO7P}},
  note         = {Machine review of arXiv:2507.10455}
}

abstract

We perform a holographic analysis of several quantum information theoretic observables entanglement entropy (EE), mutual information (MI), entanglement wedge cross section (EWCS), butterfly velocity ($v_B$) and thermo mutual information (TMI) in the background of charged AdS black hole deformed by a homogeneous string cloud. This configuration is dual to a large $\mathcal{N}_c$ strongly coupled field theory at finite temperature and finite chemical potential, in presence of quark cloud. We study how the entanglement structure and chaotic dynamics in the boundary theory are affected by the charge and backreaction. We find that both EE and EWCS increase monotonically with charge and backreaction, indicating enhanced correlations due to additional bulk degrees of freedom. On the other hand MI and TMI show a more intricate dependence backreaction tends to strengthen correlations, while increasing charge suppresses entanglement and makes the system more susceptible to scrambling. The analysis of the butterfly velocity indicates that both the presence of charge and the backreaction suppress the chaotic behavior of the system by reducing $v_B$. Furthermore, TMI exhibits a sharp transition under shockwave perturbations, with inter-boundary entanglement being entirely disrupted beyond a critical shock strength, which decreases with increasing charge.

Figures

Figures reproduced from arXiv: 2507.10455 by the authors.

**Figure 1.** Left: Variation of RT-surface for constant σ and different ρ. Right: Variation of RT-surface for fix ρ and different values of σ. From fig. 1 (left) one can see that for a finite constant σ as the value of width l increases the RT surface travels more deeper into the bulk. However, by increasing the string density ρ makes 8 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗

**Figure 2.** Left: normalized HEE (S N AB) as a function of width l at fixed temperature T = 1, backreaction ρ = 1, and charge σ = 1. Right: HEE as a function of ρ for various values of σ. HEE increases with both ρ and σ, reflecting the enhanced contribution to entanglement entropy. The behavior of the S N AB is plotted in fig. 2. This analysis reveals several important features about the entanglement structure of strongly coupl… view at source ↗

**Figure 3.** Regularized I(A : B) as a function of backreaction ρ, for different values of σ. The widths of subsystems are kept fix by fixing the corresponding turning points zt(D) = 0.01, zt(l) = 0.4 and zt(2l + D) = 0.7. The mutual information exhibits an increasing nature with ρ. Higher charge consistently reduces MI, indicating weakened inter-subsystem correlations due to additional charged degrees of freedom in the strongly… view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: Regularized EW as a function of ρ for various values of σ. EWCS increases monotonically with both ρ and σ, indicating enhanced entanglement due to additional degrees of freedom introduced by backreaction and charge. This reflects a richer entanglement structure in the …

**Figure 5.** Figure 5: The bound between Ew and I/2 for σ = 1. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

**Figure 6.** Figure 6: Left: Penrose diagram of the eternal, backreacted charged AdS black hole, with the shock wave indicated by the red line. The purple curve represents the HRT surface traversing the bifurcation point of the black hole horizon. Right: Deformed Penrose diagram illustrating…

**Figure 7.** Figure 7: Dependence of butterfly velocity vB on the backreaction parameter ρ at fixed values of the charge parameter σ. The decrease in vB with both ρ and σ reveals the impact of bulk matter fields and charge on the rate of information scrambling in the dual holographic theory.…

**Figure 8.** Figure 8: TMI as a function of subsystem width l for fixed temperature T = 1 and backreaction parameter ρ = 1, plotted for different values of the charge parameter σ. The onset of non-zero TMI occurs beyond a critical width lc, which increases with σ, indicating that charge supp…

**Figure 9.** Figure 9: Left- Regularized entanglement entropy S reg as a function of the dimensionless shockwave parameter ∆z0 = (z0 − zh)/zh for fixed backreaction ρ = 1, zh = 1 and varying charge parameter σ. The increase in S reg indicates the increase of inter-boundary entanglement due t…

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Reference graph

Works this paper leans on

58 extracted references · 21 canonical work pages

[48]

Charged AdS Black Holes in Presence of String Cloud and Cardy-Verlinde Formula

R. Pokhrel and T.K. Dey,Charged AdS black holes in presence of string cloud and Cardy-Verlinde formula, Nucl. Phys. B1001 (2024) 116508 [2303.02702]

work page Pith review arXiv 2024
[1]

Maldacena,The Large N limit of superconformal field theories and supergravity, Adv

J.M. Maldacena,The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys.2 (1998) 231 [hep-th/9711200]

arXiv 1998
[2]

Vidal and R.F

G. Vidal and R.F. Werner,Computable measure of entanglement, Phys. Rev. A65 (2002) 032314 [quant-ph/0102117]

arXiv 2002
[3]

Plenio,Logarithmic Negativity: A Full Entanglement Monotone That is not Convex, Phys

M.B. Plenio,Logarithmic Negativity: A Full Entanglement Monotone That is not Convex, Phys. Rev. Lett.95 (2005) 090503 [quant-ph/0505071]

arXiv 2005
[4]

Terhal, M

B.M. Terhal, M. Horodecki, D.W. Leung and D.P. DiVincenzo,The entanglement of purification, J. Math. Phys.43 (2002) 4286 [quant-ph/0202044]

arXiv 2002
[5]

Dutta and T

S. Dutta and T. Faulkner,A canonical purification for the entanglement wedge cross-section, JHEP 03 (2021) 178 [1905.00577]

arXiv 2021
[6]

Witten,Anti-de Sitter space and holography, Adv

E. Witten,Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253 [hep-th/9802150]

arXiv 1998
[7]

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]

arXiv 2006

Show all 58 references

[8]

Ryu and T

S. Ryu and T. Takayanagi,Aspects of Holographic Entanglement Entropy, JHEP 08 (2006) 045 [hep-th/0605073]

2006 arXiv
[9]

Hubeny, M

V.E. Hubeny, M. Rangamani and T. Takayanagi,A Covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [0705.0016]

2007 arXiv
[10]

Takayanagi and K

T. Takayanagi and K. Umemoto,Entanglement of purification through holographic duality, Nature Phys.14 (2018) 573 [1708.09393]

2018 arXiv
[11]

Nguyen, T

P. Nguyen, T. Devakul, M.G. Halbasch, M.P. Zaletel and B. Swingle,Entanglement of purification: from spin chains to holography, JHEP 01 (2018) 098 [1709.07424]

2018 arXiv
[12]

Shenker and D

S.H. Shenker and D. Stanford,Black holes and the butterfly effect, JHEP 03 (2014) 067 [1306.0622]

2014 arXiv
[13]

Shenker and D

S.H. Shenker and D. Stanford,Multiple shocks, JHEP 12 (2014) 046 [1312.3296]

2014 arXiv
[14]

Hartman and J

T. Hartman and J. Maldacena,Time evolution of entanglement entropy from black hole interiors, JHEP 05 (2013) 014 [1303.1080]

2013 arXiv
[15]

Shenker and D

S.H. Shenker and D. Stanford,Stringy effects in scrambling, JHEP 05 (2015) 132 [1412.6087]

2015 arXiv
[16]

Roberts, D

D.A. Roberts, D. Stanford and L. Susskind,Localized shocks, JHEP 03 (2015) 051 [1409.8180]. 24

2015 arXiv
[17]

Fischler, V

W. Fischler, V. Jahnke and J.F. Pedraza,Chaos and entanglement spreading in a non-commutative gauge theory, JHEP 11 (2018) 072 [1808.10050]

2018 arXiv
[18]

Jahnke,Delocalizing entanglement of anisotropic black branes, JHEP 01 (2018) 102 [1708.07243]

V. Jahnke,Delocalizing entanglement of anisotropic black branes, JHEP 01 (2018) 102 [1708.07243]

2018 arXiv
[19]

Maldacena,Eternal black holes in anti-de sitter, JHEP 04 (2003) 021 [hep-th/0106112]

J. Maldacena,Eternal black holes in anti-de sitter, JHEP 04 (2003) 021 [hep-th/0106112]

2003 arXiv
[20]

Morrison and M.M

I.A. Morrison and M.M. Roberts,Mutual information between thermo-field doubles and disconnected holographic boundaries, JHEP 07 (2013) 081 [1211.2887]

2013 arXiv
[21]

Liu and S.J

H. Liu and S.J. Suh,Entanglement tsunami: Universal scaling in holographic thermalization, Phys. Rev. Lett.112 (2014) 011601 [1305.7244]

2014 arXiv
[22]

Leichenauer,Disrupting entanglement of black holes, Phys

S. Leichenauer,Disrupting entanglement of black holes, Phys. Rev. D90 (2014) 046009 [1405.7365]

2014 arXiv
[23]

Jahnke,Recent developments in the holographic description of quantum chaos, Adv

V. Jahnke,Recent developments in the holographic description of quantum chaos, Adv. High Energy Phys.2019 (2019) 9632708 [1811.06949]

2019 arXiv
[24]

Li, B.-Q

H.-L. Li, B.-Q. Zhang, X.-M. Jiao and W.-J. Feng,Mutual correlation and chaotic behavior in phantom AdS black holes in both dynamic and static backgrounds, Results Phys.64 (2024) 107895

2024
[25]

Saha and S

A. Saha and S. Gangopadhyay,Quantum chaos in the presence of nonconformality, Phys. Rev. D110 (2024) 026025 [2401.05814]

2024 arXiv
[26]

Karan and S

D. Karan and S. Pant,Entanglement and Chaos near critical point in strongly coupled Gauge theory, Eur. Phys. J. C84 (2024) 113 [2308.00018]

2024 arXiv
[27]

K. Sil, S. Maji, S. Christodoulou and A. Chowdhury,Information scrambling with higher-form fields, JHEP 02 (2025) 008 [2410.04625]

2025 arXiv
[28]

Mahish and K

S. Mahish and K. Sil,Quantum information scrambling and quantum chaos in little string theory, JHEP 08 (2022) 041 [2202.05865]

2022 arXiv
[29]

Sil,Pole skipping and chaos in anisotropic plasma: a holographic study, JHEP 03 (2021) 232 [2012.07710]

K. Sil,Pole skipping and chaos in anisotropic plasma: a holographic study, JHEP 03 (2021) 232 [2012.07710]

2021 arXiv
[30]

Baishya, A

B. Baishya, A. Chakraborty and N. Padhi,Entanglement wedge method, out-of-time-ordered correlators, and pole skipping, Phys. Rev. D111 (2025) 106013 [2406.18319]

2025 arXiv
[31]

W.Z. Chua, T. Hartman and W.W. Weng,Replica manifolds, pole skipping, and the butterfly effect, 2504.08139

arXiv
[32]

Singh, A

A. Singh, A. Modak and B. Panda,A Note on Chaos in Hayward Black Holes with String Fluids, 2507.02716

arXiv
[33]

D. Basu, A. Chandra and Q. Wen,Butterfly effect and TT-deformation, 2505.14331

arXiv
[34]

Lilani, D

N. Lilani, D. Sandhu and S. Mahapatra,Comparative study of the butterfly velocity in holographic QCD models at finite temperature and chemical potential, 2505.15357

arXiv
[35]

Casini, M

H. Casini, M. Huerta and R.C. Myers,Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [1102.0440]

2011 arXiv
[36]

Jensen and A

K. Jensen and A. O’Bannon,Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects, Phys. Rev. D88 (2013) 106006 [1309.4523]. 25

2013 arXiv
[37]

Rodgers,Holographic entanglement entropy from probe M-theory branes, JHEP 03 (2019) 092 [1811.12375]

R. Rodgers,Holographic entanglement entropy from probe M-theory branes, JHEP 03 (2019) 092 [1811.12375]

2019 arXiv
[38]

Carmi,On the Shape Dependence of Entanglement Entropy, JHEP 12 (2015) 043 [1506.07528]

D. Carmi,On the Shape Dependence of Entanglement Entropy, JHEP 12 (2015) 043 [1506.07528]

2015 arXiv
[39]

Carmi,More on Holographic Volumes, Entanglement, and Complexity, 1709.10463

D. Carmi,More on Holographic Volumes, Entanglement, and Complexity, 1709.10463

arXiv
[40]

Hung, R.C

L.-Y. Hung, R.C. Myers and M. Smolkin,Some Calculable Contributions to Holographic Entanglement Entropy, JHEP 08 (2011) 039 [1105.6055]

2011 arXiv
[41]

Kontoudi and G

K. Kontoudi and G. Policastro,Flavor corrections to the entanglement entropy, JHEP 01 (2014) 043 [1310.4549]

2014 arXiv
[42]

Chakrabortty,Dissipative force on an external quark in heavy quark cloud, Phys

S. Chakrabortty,Dissipative force on an external quark in heavy quark cloud, Phys. Lett. B 705 (2011) 244 [1108.0165]

2011 arXiv
[43]

Chakrabortty and T.K

S. Chakrabortty and T.K. Dey,Back reaction effects on the dynamics of heavy probes in heavy quark cloud, JHEP 05 (2016) 094 [1602.04761]

2016 arXiv
[44]

Chakrabortty, S

S. Chakrabortty, S. Pant and K. Sil,Effect of back reaction on entanglement and subregion volume complexity in strongly coupled plasma, JHEP 06 (2020) 061 [2004.06991]

2020 arXiv
[45]

Chakrabortty, H

S. Chakrabortty, H. Hoshino, S. Pant and K. Sil,A holographic study of the characteristics of chaos and correlation in the presence of backreaction, Phys. Lett. B838 (2023) 137749 [2206.12555]

2023 arXiv
[46]

P. Jain, S. Pant and H. Parihar,Effect of backreaction on island, Page curve and mutual information, Nucl. Phys. B1018 (2025) 116991 [2311.08186]

2025 arXiv
[47]

Dey and S

T.K. Dey and S. Mukhopadhyay,AdS black holes with higher derivative corrections in presence of string cloud, Eur. Phys. J. C80 (2020) 1012 [2005.12054]

2020 arXiv
[49]

Dey and S

T.K. Dey and S. Mukhopadhyay,Charged AdS black holes with higher derivative corrections in presence of string cloud, 2302.00256

arXiv
[50]

Letelier,CLOUDS OF STRINGS IN GENERAL RELATIVITY, Phys

P.S. Letelier,CLOUDS OF STRINGS IN GENERAL RELATIVITY, Phys. Rev. D20 (1979) 1294

1979
[51]

Herscovich and M.G

E. Herscovich and M.G. Richarte,Black holes in Einstein-Gauss-Bonnet gravity with a string cloud background, Phys. Lett. B689 (2010) 192 [1004.3754]

2010 arXiv
[52]

Stanford and L

D. Stanford and L. Susskind,Complexity and Shock Wave Geometries, Phys. Rev. D90 (2014) 126007 [1406.2678]

2014 arXiv
[53]

Israel,Thermo field dynamics of black holes, Phys

W. Israel,Thermo field dynamics of black holes, Phys. Lett. A57 (1976) 107

1976
[54]

Dray and G

T. Dray and G. ’t Hooft,The gravitational shock wave of a massless particle, Nuclear Physics B 253 (1985) 173

1985
[55]

Sfetsos,On gravitational shock waves in curved space-times, Nucl

K. Sfetsos,On gravitational shock waves in curved space-times, Nucl. Phys. B436 (1995) 721 [hep-th/9408169]

1995 arXiv
[56]

Mezei,On entanglement spreading from holography, JHEP 05 (2017) 064 [1612.00082]

M. Mezei,On entanglement spreading from holography, JHEP 05 (2017) 064 [1612.00082]. 26

2017 arXiv
[57]

Mezei and D

M. Mezei and D. Stanford,On entanglement spreading in chaotic systems, JHEP 05 (2017) 065 [1608.05101]

2017 arXiv
[58]

Liu and S.J

H. Liu and S.J. Suh,Entanglement growth during thermalization in holographic systems, Phys. Rev. D89 (2014) 066012 [1311.1200]. 27

2014 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [48]

Charged AdS Black Holes in Presence of String Cloud and Cardy-Verlinde Formula

R. Pokhrel and T.K. Dey,Charged AdS black holes in presence of string cloud and Cardy-Verlinde formula, Nucl. Phys. B1001 (2024) 116508 [2303.02702]

work page Pith review arXiv 2024

[2] [1]

Maldacena,The Large N limit of superconformal field theories and supergravity, Adv

J.M. Maldacena,The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys.2 (1998) 231 [hep-th/9711200]

arXiv 1998

[3] [2]

Vidal and R.F

G. Vidal and R.F. Werner,Computable measure of entanglement, Phys. Rev. A65 (2002) 032314 [quant-ph/0102117]

arXiv 2002

[4] [3]

Plenio,Logarithmic Negativity: A Full Entanglement Monotone That is not Convex, Phys

M.B. Plenio,Logarithmic Negativity: A Full Entanglement Monotone That is not Convex, Phys. Rev. Lett.95 (2005) 090503 [quant-ph/0505071]

arXiv 2005

[5] [4]

Terhal, M

B.M. Terhal, M. Horodecki, D.W. Leung and D.P. DiVincenzo,The entanglement of purification, J. Math. Phys.43 (2002) 4286 [quant-ph/0202044]

arXiv 2002

[6] [5]

Dutta and T

S. Dutta and T. Faulkner,A canonical purification for the entanglement wedge cross-section, JHEP 03 (2021) 178 [1905.00577]

arXiv 2021

[7] [6]

Witten,Anti-de Sitter space and holography, Adv

E. Witten,Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253 [hep-th/9802150]

arXiv 1998

[8] [7]

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]

arXiv 2006