Holographic superconductor with dark matter probed by entanglement entropy in higher dimensional AdS spacetime

Weiping Yao; Yifu Cai; Zehua Tian

REVIEW 4 major objections 5 minor 77 references

Holographic superconductor with dark matter probed by entanglement entropy in higher dimensional AdS spacetime

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read In a five-dimensional curved black-hole spacetime with an extra hidden gauge field, the entanglement entropy of a boundary strip pinpoints the superconducting transition temperature and its order, and its critical value grows linearly…

desk verdict Plausible extension with a fresh scaling claim, but the printed equations and HEE formula do not match the numerics, so the results are unverified. read the letter →

arxiv 2505.20677 v1 pith:KM6YQBQ4 submitted 2025-05-27 hep-th

Weiping Yao , Yifu Cai , Zehua Tian This is my paper · ORCID

classification hep-th

keywords AdS/CFTcorrespondenceholographicsuperconductorentanglemententropydarkmattersectorhiddenU(1)gaugefieldphasetransitioncriticaltemperaturehigher-dimensionalSspacetime

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

Using a five-dimensional anti-de Sitter (AdS) black hole with full backreaction, this paper tries to establish that holographic entanglement entropy (HEE) is a reliable probe of the metal/superconductor transition when a hidden dark-matter gauge field is coupled to the visible Maxwell sector. The authors compute both the scalar condensate and the HEE of a boundary strip, and they find that the critical temperature read off from HEE matches the critical temperature of scalar condensation. They also report that the HEE is continuous but has a discontinuous temperature derivative at the transition, indicating a second-order transition, and that the critical HEE grows linearly with the dark-matter coupling $\alpha$ while increasing nonlinearly and with accelerating slope as the chemical-potential ratio $\xi/\mu$ grows. If correct, this gives a boundary quantity that not only locates the phase transition but can distinguish which dark-sector parameter is driving it.

What carries the argument

The load-bearing object is the holographic entanglement entropy of a strip of width $\ell$, computed with the Ryu-Takayanagi area prescription $S_A=\mathrm{Area}(\gamma_A)/(4G_N)$, where $\gamma_A$ is the minimal surface in the bulk ending on the strip boundary. The bulk model is the Einstein-Maxwell-scalar system with an additional hidden U(1) gauge field $B_{\mu\nu}$ and kinetic mixing term $-\frac{\alpha}{4}F_{\mu\nu}B^{\mu\nu}$, solved numerically by a shooting method from the horizon to the AdS boundary after fixing $r_+=1$ and $L=1$. The argument then compares two readings of the phase transition: the temperature where the scalar condensate $\langle O_+\rangle$ turns on, and the temperature where the HEE slope is discontinuous; the reported tables show these agree.

What would settle it

Re-derive the $z$-coordinate equations from the $r$-space equations of motion, solve the corrected system with the same boundary conditions, and check whether the reported critical temperatures and the linear-in-$\alpha$, nonlinear-in-$\xi/\mu$ HEE scalings are reproduced. If they are not, the central claim is refuted.

Watch

Extended reading notes

Core claim

The central claim is that the holographic entanglement entropy of a strip-shaped boundary region in a fully backreacted five-dimensional AdS black hole with a hidden U(1) dark-matter sector behaves as a diagnostic of the holographic superconductor phase transition. Below the critical temperature $T_c$, the HEE is lower than in the normal phase and falls more steeply as temperature decreases; at $T_c$ it is continuous while its slope jumps, which the authors read as a second-order transition. Numerically, the critical temperatures obtained from HEE agree exactly with those obtained from the scalar operator for all tested values of the dark-matter coupling $\alpha$ and the chemical-potential ratio $\xi/\mu$, and both parameters lower $T_c$ when increased. The distinctive new result is the critical behavior: near $T_c$, the critical HEE $s_c$ grows linearly with $\alpha$ but in a nonlinear, accelerated way with $\xi/\mu$, while a larger strip width $\ell$ suppresses the growth of $s_c$ without changing $T_c$.

Load-bearing premise

The numerical results stand on the assumption that the computer code solves the exact equations the stated model requires, even though the coordinate-transformed equations printed in the paper do not match the original ones.

Editorial extensions

If this is right

The HEE can be used instead of the scalar condensate to locate $T_c$, because the two methods agree to the precision shown in Tables 1 and 2.
The jump in the temperature derivative of the HEE at $T_c$ provides a holographic signature that the transition is second order.
Stronger dark-matter coupling $\alpha$ and larger chemical-potential ratio $\xi/\mu$ both lower $T_c$, meaning the dark sector makes the superconducting phase harder to form.
At the transition, the HEE distinguishes the dark-sector parameters: it grows linearly with $\alpha$, nonlinearly and faster with $\xi/\mu$, while the strip width $\ell$ acts in the opposite direction by suppressing the growth rate of $s_c$.

Reading between the lines

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

Beyond the paper: because $\alpha$ and $\xi/\mu$ imprint different functional forms on the critical entanglement entropy, a boundary observer who can measure $s_c$ across temperatures could in principle infer both dark-sector parameters separately.
A testable extension the paper leaves implicit is whether $s_c$ collapses onto a single curve when expressed in terms of the effective charge combination $\rho^2+\alpha\rho\rho_d+\rho_d^2$ rather than in terms of $\alpha$ and $\xi/\mu$ separately.
The analysis uses a strip entangling region; repeating the calculation for spherical or annular regions would show whether the linear-versus-nonlinear distinction is a universal critical signature or a property of the strip geometry.

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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

Here is my take. The paper extends a known 4D probe-limit calculation of holographic entanglement entropy in a dark-matter superconductor to 5D with full backreaction. The genuinely new item is the claim that near the transition the critical HEE grows linearly with the dark-matter coupling α and nonlinearly with the chemical-potential ratio ξ/μ. That parametric behavior is not in the earlier literature, so there is a real result if the numerics hold up.

The qualitative physics is sensible: Tc decreases as α or ξ/μ increases, matching the 4D behavior and physical intuition. The paper is readable, and the agreement between Tc extracted from HEE and from the scalar operator is a reasonable consistency check. I do not count that as a serious flaw; it is standard practice in this area.

The problems are in the equations, and they are load-bearing. The z-coordinate equations of motion (3.3)-(3.5) do not follow from the r-space system (2.5)-(2.9) under z=1/r. I checked the transformation directly: the gauge and mass terms have wrong coefficients and signs. Independently, the HEE integral (4.7) has the wrong power of z in the integrand. The correct reduction from (4.5) gives a denominator with z^4 sqrt(f) sqrt(z_*^6-z^6); the displayed version has z^3. In pure AdS the displayed integral diverges as 1/ε, while the paper's own final form requires 1/ε^2. So the printed HEE formula cannot produce the stated area-law divergence. Either the code used a corrected formula that is not in the manuscript, or the figures were computed from a formula different from the one shown. No code or data are provided, so I cannot tell which.

Because the scaling claims in Figure 3 are numerical read-offs from this unreproducible pipeline, they are not established. The circularity of computing HEE from the same metric that defines the transition is real but minor; it is a consistency check, not an independent prediction.

Who gets value from this? Researchers who care about the qualitative effect of a dark sector on holographic superconductors, but only after the equations are corrected and reproducibility artifacts are released. I would not cite the scaling result now. As a referee assignment, I would send it to review: the question is legitimate, the errors look fixable, and a referee can require the corrected equations and the numerical code before acceptance. It is not ready as is.

Referee Report

4 major / 5 minor

Summary. The manuscript studies a five-dimensional holographic superconductor with an additional hidden U(1) dark-matter sector, including full backreaction of the matter fields on the AdS black hole geometry. The authors write down Einstein-Maxwell-scalar-dark matter equations of motion, solve them numerically by a shooting method in the z=1/r coordinate, compute the scalar condensate, and then evaluate the holographic entanglement entropy (HEE) for a strip geometry. The main reported results are that the critical temperature decreases with the dark-matter coupling α and with the chemical-potential ratio ξ/μ; that the HEE is continuous at the critical point with a discontinuous slope, indicating a second-order transition; and that the critical HEE grows linearly with α but nonlinearly and in an accelerated way with ξ/μ, while larger strip width suppresses the growth. The abstract's central novelty is this scaling behavior of the critical HEE.

Significance. If the numerical results are correct, the paper would extend earlier four-dimensional holographic dark-matter superconductor studies to five dimensions and would offer a concrete parametric signature that distinguishes the dark-matter coupling from the chemical-potential imbalance. The claimed linear-in-α versus nonlinear-in-ξ/μ behavior of the critical HEE is a falsifiable prediction within the model and is interesting enough to warrant careful verification. However, the evidence is entirely numerical and, as detailed below, the printed equations are internally inconsistent, so the results are not yet established. The paper does not provide machine-checked code or parameter-free derivations; its strengths are the clear physical question and the potentially distinctive scaling claim.

major comments (4)

[Section 3, Eqs. (3.3)-(3.7)] The z-coordinate equations of motion are not the z=1/r transforms of the r-space equations (2.5)-(2.9). For example, applying z=1/r to Eq. (2.6) gives f_z + (4/z^3 - 2f/z) - (1/(3z))[m^2 ψ^2 + z^4 f ψ_z^2 + q^2 e^χ φ^2 ψ^2/f + (z^4/2)e^χ(φ_z^2 + η_z(η_z + α φ_z))] = 0, whereas Eq. (3.4) has a positive matter term with prefactor 1/(3z^3) and different powers of z. Similarly, Eq. (3.5) does not follow from Eq. (2.7): the mass term and the gauge term have the wrong powers of z and signs. Since the shooting code must solve some version of these equations, the background metric used for all figures is not defined by the manuscript. The authors need to provide the corrected z-space equations and confirm that the numerical code actually solves them.
[Section 4, Eq. (4.7)] The HEE integrand displayed in Eq. (4.7) contains the wrong power of z. Variation of the area functional (4.5) gives Eq. (4.6) with r_s = r_*; substituting the resulting dx/dr into L_A and changing to z=1/r yields an area integrand proportional to z_*^3/[z^4 sqrt(f(z)) sqrt(z_*^6 - z^6)] (including the 1/z^2 Jacobian from dr), not the displayed z_*^3/[z^2 sqrt((z_*^6 - z^6) z^2 f(z))], which is one factor of z too large in the denominator. In pure AdS5, the printed integrand gives a 1/ε UV divergence, while the paper's own final expression RW/(4G5)(1/ε^2 + s) requires 1/ε^2. Therefore, either the numerical code used a corrected integrand that is not given in the text, or the HEE values and the scaling curves in Figures 2-4 were computed from the wrong formula. This must be resolved before the central scaling claim can be assessed.
[Section 3, Eqs. (3.1)-(3.2)] The claimed normal-phase solution does not solve the field equations. Inserting φ = ρ(1 - 1/(2r)) into Eq. (2.8) with ψ=0 and η=0 gives φ'' + (3/r)φ' = ρ/(2r^3) ≠ 0. The correct d=5 Reissner-Nordstrom-AdS potential with horizon at r=1 should behave as μ(1 - 1/r^2), which satisfies φ'' + (3/r)φ' = 0. The expression for f in Eq. (3.2) is also inconsistent with the f-equation (2.6) for the same reason. This is another concrete instance of the internal inconsistencies in the printed equations, and it further prevents the reader from reproducing the starting point of the numerical analysis.
[Section 4, Tables 1-2] The agreement between the critical temperatures obtained from the scalar condensate and from the HEE is presented as evidence that HEE diagnoses the phase transition, but this is not an independent check. Both quantities are evaluated on the same backreacted numerical solution, so the identical Tc values in Tables 1 and 2 are a consistency condition rather than a confirmation. The authors should rephrase this claim: the useful statement is that the HEE reproduces the same transition point and order from a geometric observable, not that the two determinations independently validate each other.

minor comments (5)

[Throughout] The scalar kinetic term in Eq. (2.1) is written as [∇_μ ψ - i q A_μ ψ]+[∇_μ ψ - i q A_μ ψ]; this should be |∇_μ ψ - i q A_μ ψ|^2 with an explicit modulus squared.
[Tables 1 and 2] The decimal commas such as '0,6', '0,8', and '1,0' are inconsistent with the decimal points used elsewhere and should be unified.
[Figures 3 and 4] The axis labels in Figures 3 and 4 are garbled in the manuscript (e.g., '/ScriptAltLΡ1/Slash13/EquΑl1.0' and '/Ξ/Slash1Μ'); they must be replaced with readable notation before publication.
[Section 2] The phrase 'additional additional hidden U(1) gauge field' contains a duplicated word and should be corrected.
[References] Reference [38] appears corrupted: 'Gauge theory correlators from noncritical string theory , A. M. Polyakov, Phys. Lett. B 428, 105-114 (1998)' should be split into the correct Gubser-Klebanov-Polyakov citation with the authors properly listed.

Circularity Check

1 steps flagged · score 3.0 of 10

Mild tautology in the HEE/T_c cross-check; the central HEE scaling results are not circular, though they rest on an unverified integral.

other [Section 4, text after Fig. 2 and Tables 1-2]
"in the tables 1 and 2, we obtain the critical temperature from the analysis of the the HEE, and compare them with that from analyzing the behaviors of the scalar operator. We observe that the critical temperature obtained from these two different physical scenarios are completely consistent."

The HEE is evaluated on the same numerical backreacted metric that defines the superconducting transition through the scalar condensate. Both T_c values are therefore read from one and the same solution of the coupled equations, so the equality in Tables 1-2 is guaranteed by construction rather than being an independent cross-check of two 'different physical scenarios'. No external data or independent calculation enters the comparison; the HEE adds no new information about the location of the critical point, only about the behavior of another functional of the same geometry.

full rationale

The construction is otherwise self-contained: the model action is stated, the equations of motion are written down, and the numerical background is used to compute both the scalar operator and the HEE. No fitted parameter is recycled into a 'prediction', and the dark-matter dependence of the critical HEE (Fig. 3) is a direct numerical read-off, not a quantity that is equivalent to an input by definition. The only self-citation, Ref. [77] used as a no-dark-matter benchmark, is not load-bearing for the central dark-matter results. The apparent mismatch between Eq. (4.7) and the minimal-area Lagrangian (4.5), and the inconsistency between the z-space EOMs (3.3)-(3.5) and the r-space system, are serious reproducibility/correctness defects, but they are errors in derivation rather than circularity: an incorrect integral does not make the claimed scaling tautological, it makes it unsupported. Overall, the paper has one mild tautological consistency check but no central circularity; the novel scaling claims are not forced by a fit or by definition.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The model uses a pre-existing dark matter gauge sector and standard holographic tools. No new entities are invented. The free-parameter list is empty because alpha and xi/mu are scanned model parameters, not fitted values. The main unstated burden is the correctness of the numerical background solutions, which the printed equations do not support.

assumptions (6)

domain assumption AdS/CFT correspondence maps the 5D gravitational system to a strongly coupled boundary field theory.
Invoked throughout Section 1, Refs. [37-39].
domain assumption Ryu-Takayanagi proposal: entanglement entropy of a boundary region equals the minimal area in the bulk.
Section 4, Eq. (4.1), Refs. [49,50].
domain assumption Dark matter sector is modeled as a hidden U(1) gauge field with kinetic mixing alpha with the Maxwell field.
Section 2, Eq. (2.1), from Refs. [42,43].
domain assumption Matter fields have only temporal components that are real functions of r.
Section 2, Eq. (2.4); standard ansatz, but restricts the solution space.
domain assumption Boundary condition psi_- = 0, psi_+ normalizable, and q=2, m^2=-15/4 are chosen.
Section 3; these choices fix the operator and simplify numerics.
standard math Scaling symmetries can set r_+ = 1 and L = 1.
Section 2, Eqs. (2.12)-(2.13); standard in such systems.

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Cite this review

Pith. "Pith review of Holographic superconductor with dark matter probed by entanglement entropy in higher dimensional AdS spacetime." pith.science (2026). https://pith.science/paper/KM6YQBQ4

@misc{pith2026250520677,
  author       = {Pith},
  title        = {Pith review of: Holographic superconductor with dark matter probed by entanglement entropy in higher dimensional AdS spacetime},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KM6YQBQ4}},
  note         = {Machine review of arXiv:2505.20677}
}

read the original abstract

We investigate the holographic entanglement entropy (HEE) with dark matter in a higher-dimensional AdS black hole spacetime including full back reaction, revealing its role as a diagnostic tool for critical phenomena in strongly coupled systems. By analyzing the HEE, we uncover distinct signatures of the metal/superconductor phase transition, demonstrating that the critical temperature is dynamically tuned by both the dark matter coupling strength and the chemical potential ratio between visible and dark matter sectors. Notably, near the criticality, the HEE exhibits a novel scaling behavior: it grows linearly with the dark matter coupling but displays a nonlinear, accelerated enhancement as the chemical potential ratio between the Maxwell and dark matter sectors increases.

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

77 extracted references · 73 canonical work pages

[1]

Corbelli and P

E. Corbelli and P. Salucci, The Extended Rotation Curve and the Dark Matter Halo of M33 , Adv. Theor. Math. Phys. 2, 231-252 (1998), arXiv:astro-ph/9909252 [astro-ph]

arXiv 1998
[2]

Vikhlinin, A

A. Vikhlinin, A. Kravtsov, W. Forman, C. Jones, M. Markevitch, S . S. Murray, and L. Van Speybroeck, Chandra sample of nearby relaxed galaxy clusters: mass, gas fraction, and mass-temperature relation, Astrophys. J. 640, 691 (2006), arXiv:astro-ph/0507092 [astro-ph]

arXiv 2006
[3]

Clowe, M

D. Clowe, M. Bradac, A. H. Gonzalez, M. Markevitch, S. W. Randa ll, C. Jones, and D. Zaritsky, CA direct empirical proof of the existence of dark matter , Astrophys. J. 648, L109-L113 (2006), arXiv:astro-ph/0608407 [astro-ph]

arXiv 2006
[5]

P. A. R. Ade, N. Aghanim, Z. Ahmed, R. W. Aikin, K. D. Alexander, M . Arnaud, J. Aumont, C. Baccigalupi, A. J. Banday et al. (BICEP2/Keck and Planck Collabor ations), Joint Analysis of BICEP2/Keck Array and Planck Data , Phys. Rev. Lett. 114, 101301 (2015), arXiv:1502.01589 [astro-ph.CO]

arXiv 2015
[6]

Wagner, G

ADMX Collaboration, A. Wagner, G. Rybka, M. Hotz, L. J. Rosenb erg, S. J. Asztalos, G. Carosi et al., A Search for Hidden Sector Photons with ADMX , Phys. Rev. Lett. 105,171801 (2010)

work page 2010
[7]

Horns, J

D. Horns, J. Jaeckel, A. Lindner, A. Lobanov, J. Redondo and A . Ringwald, Searching for WISPy Cold Dark Matter with a Dish Antenna , JCAP 04, 016 (2013)

work page 2013
[8]

P. W. Graham, J. Mardon, S. Rajendran and Y. Zhao, Parametrically enhanced hidden photon search, Phys. Rev. D 90, 075017 (2014)

work page 2014
[9]

Chaudhuri, P

S. Chaudhuri, P. W. Graham, K. Irwin, J. Mardon, S. Rajendran and Y. Zhao, Radio for hidden-photon dark matter detection , Phys. Rev. D 92, 075012 (2015)

work page 2015

Show all 77 references

[10]

P. W. Graham, D. E. Kaplan, J. Mardon, S. Rajendran and W. A. Terrano, Dark matter direct detection with accelerometers , Phys. Rev. D 93, 075029 (2016)

2016
[11]

Caldwell, G

MADMAX Working Group, A. Caldwell, G. Dvali, B. Majorovits, A. Milla r, G. Raﬀelt, J. Redondo et al., Dielectric Haloscopes: A New Way to Detect Axion Dark Matter , Phys. Rev. Lett. 118, 091801 (2017)

2017
[12]

Anastassopoulos, S

CAST, V. Anastassopoulos, S. Aune, K. Barth, A. Belov, H. B¨ rauninger, G. Cantatore et al., New CAST limit on the axion-photon interaction , Nature Phys. 13, 584590 (2017)

2017
[13]

Baryakhtar, J

M. Baryakhtar, J. Huang and R. Lasenby, Axion and hidden photon dark matter detection with multilayer optical haloscopes , Phys. Rev. D 98, 035006 (2018)

2018
[14]

Lawson, A

M. Lawson, A. J. Millar, M. Pancaldi, E. Vitagliano and F. Wilczek, Tunable axion plasma haloscopes, Phys. Rev. Lett. 123, 141802 (2019)

2019
[15]

Andrianavalomahefa, C

FUNK Experiment, A. Andrianavalomahefa, C. M. Sch¨ afer, D. Veberiˇc, R. Engel, T. Schwetz, H.-J. Mathes et al., Limits from the Funk Experiment on the Mixing Strength of Hid den-Photon Dark Matter in the Visible and Near-Ultraviolet Wavelength Range, Phys. Rev. D 102, 042001 (2020)

2020
[16]

G. B. Gelmini, A. J. Millar, V. Takhistov and E. Vitagliano, Probing dark photons with plasma haloscopes, Phys. Rev. D 102, 043003 (2020). – 10 –

2020
[17]

A. V. Gramolin, D. Aybas, D. Johnson, J. Adam and A. O. Sushko v, Search for axion-like dark matter with ferromagnets , Nat. Phys. 17, 79 (2021)

2021
[18]

L. Su, L. Wu and B. Zhu, Probing for an ultralight dark photon from inverse compton- like scattering, Phys. Rev. D 105, 055021 (2022)

2022
[19]

Chiles, I

J. Chiles, I. Charaev, R. Lasenby, M. Baryakhtar, J. Huang, A. Roshko et al., New constraints on dark photon dark matter with superconducting nanowire de tectors in an optical haloscope , Phys. Rev. Lett. 128, 231802 (2022)

2022
[20]

Romanenko, R

A. Romanenko, R. Harnik, A. Grassellino, R. Pilipenko, Y. Pischaln ikov, Z. Liu et al.,, Search for dark photons with superconducting radio frequency cavi ties, Phys. Rev. Lett. 130, 261801(2023)

2023
[21]

Gerard Higgins, Saarik Kalia, Zhen Liu, Maglev for Dark Matter: Dark-photon and axion dark matter sensing with levitated superconductors , Phys. Rev. D 109, 055024 (2024)

2024
[22]

Blais, R.-S

A. Blais, R.-S. Huang, A. Wallraﬀ, S. M. Girvin, and R. J. Schoelkop f, Cavity quantum electrodynamics for superconducting electrical circuits : An architecture for quantum computation, Phys. Rev. A 69, 062320 (2004)

2004
[23]

Megrant et al., Planar superconducting resonators with internal quality f actors above one million, Phys

A. Megrant et al., Planar superconducting resonators with internal quality f actors above one million, Phys. Lett. 100, 113510 (2012)

2012
[24]

Bertone and T

G. Bertone and T. M. P. Tait, A new era in the search for dark matter , Nature 562, 51 (2018)

2018
[25]

Hochberg, T

Y. Hochberg, T. Lin, and K. M. Zurek, Detecting ultralight bosonic dark matter via absorptionin superconductors, Phys. Rev. D 94, 015019 (2016)

2016
[26]

Knapen, T

S. Knapen, T. Lin, and K. M. Zurek, Light dark matter in superﬂuid helium: Detection with multi-excitation production, Phys. Rev. D 95, 056019 (2017)

2017
[27]

Knapen, T

S. Knapen, T. Lin, M. Pyle, and K. M. Zurek, Detection of light dark matter with optical phonons in polar materials , Phys. Lett. B 785, 386 (2018)

2018
[28]

Budnik, O

R. Budnik, O. Cheshnovsky, O. Slone, and T. Volansky, Direct detection of light dark matter and solar neutrinos via color center production in crystals , Phys. Lett. B 782, 242 (2018)

2018
[29]

Iwazaki, A new method for detecting axion with cylindrical supercond uctor, Phys

A. Iwazaki, A new method for detecting axion with cylindrical supercond uctor, Phys. Lett. B 811, 135861 (2020)

2020
[30]

A Iwazaki, Axion-radiation conversion by super and normal conductors , Nucl. Phys. B 963, 115298 (2021)

2021
[31]

A. V. Dixit, S. Chakram, K. He, A. Agrawal, R. K. Naik, D. I. Schu ster, and A. Chou, Searching for dark matter with a superconducting qubit , Phys. Rev. Lett. 126, 141302 (2021)

2021
[32]

Z. Wang, F. Kong, P. Zhao, Z. Huang, P. Yu, Y. Wang, F. Shi, an d J. Du,, Picotesla magnetometry of microwave ﬁelds with diamond sensors , Sci. Adv. 8, eabq8158 (2022)

2022
[33]

S. Chen, H. Fukuda, T. Inada, T. Moroi, T. Nitta, and T. Sichan ugrist, Detecting Hidden Photon Dark Matter Using the Direct Excitation of Transmon Q ubits, Phys. Rev. Lett. 131, 211001 (2023)

2023
[34]

Acharya et al., Suppressing quantum errors by scaling a surface code logica l qubit , Nature 614, 676-681 (2023)

R. Acharya et al., Suppressing quantum errors by scaling a surface code logica l qubit , Nature 614, 676-681 (2023)

2023
[35]

Agrawal, A

A. Agrawal, A. V. Dixit, T. Roy, S. Chakram, K. He, R. K. Naik, D. I. Schuster, and A. Chou, Stimulated Emission of Signal Photons from Dark Matter Wave s, Phys. Rev. Lett. 132, 140801 (2024)

2024
[36]

Caldwell, Cold Dark Matter Based on an Analogy with Superconductivity, Phys

Guanming Liang, Robert R. Caldwell, Cold Dark Matter Based on an Analogy with Superconductivity, Phys. Rev. Lett. 134, 191004(2025). – 11 –

2025
[37]

J. M. Maldacena, The large N limit of superconformal ﬁeld theories andsuperg ravity, Adv. Theor. Math. Phys. 2, 231-252 (1998)

1998
[38]

S. S. Gubser and I. R. Klebanov, Gauge theory correlators from noncritical string theory , A. M. Polyakov, Phys. Lett. B 428, 105-114 (1998)

1998
[39]

Witten, Anti-de Sitter space and holography , Adv

E. Witten, Anti-de Sitter space and holography , Adv. Theor. Math. Phys. 2, 253-291 (1998)

1998
[40]

Lukasz Nakonieczny and Marek Rogatko, Analytic study on backreacting holographic superconductors with dark matter sector , Phys. Rev. D 90, 106004 (2014)

2014
[41]

Wysokinski, Magnetic ﬁeld in holographic superconductor with dark matter sector , Phys

Lukasz Nakonieczny, Marek Rogatko and Karol I. Wysokinski, Magnetic ﬁeld in holographic superconductor with dark matter sector , Phys. Rev. D 91, 046007 (2015)

2015
[42]

Vachaspati and A

T. Vachaspati and A. Achucarro, Semilocal cosmic strings , Phys. Rev. D 44, 3067 (1991)

1991
[43]

Achucarro and T

A. Achucarro and T. Vachaspati, Semilocal and electroweak strings , Phys. Reports 327, 347 (2000)

2000
[44]

Jean et al., Early SPI/INTEGRAL measurements of 511 keV line emission fr om the 4th quadrant of the Galaxy , Astron

P. Jean et al., Early SPI/INTEGRAL measurements of 511 keV line emission fr om the 4th quadrant of the Galaxy , Astron. Astrophys. 407, L55 (2003)

2003
[45]

Chang et al., An excess of cosmic ray electrons at energies of 300-800 GeV , Nature 456, 362 (2008)

J. Chang et al., An excess of cosmic ray electrons at energies of 300-800 GeV , Nature 456, 362 (2008)

2008
[46]

Adriani et al

O. Adriani et al. (PAMELA Collaboration), An anomalous positron abundance in cosmic rays with energies 1.5-100 Gev , Nature 458, 60 (2009)

2009
[47]

Katz and F

D. Katz and F. Kurata, Retrograde condensation, Ind. Eng. Chem. 32, pp. 817-827 (1940)

1940
[48]

Aprile, D

F. Aprile, D. Roest, and J. G. Russo, Holographic superconductors from gauged supergravity , J. High Energy Phys. 06, 040 (2011)

2011
[49]

Ryu and T

S. Ryu and T. Takayanagi, Entanglement entropy and the Berry phase in the solid state Phys. Rev. Lett. 96, 181602 (2006)

2006
[50]

Ryu and T

S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy , J. High Energy Phys. 0608, 045 (2006)

2006
[51]

29, 153001 (2012)

Tadashi Takayanagi, Entanglement Entropy from a Holographic Viewpoint , Class.Quant.Grav. 29, 153001 (2012)

2012
[52]

Rong-Gen Cai, Song He, Li Li, Yun-Long Zhang, Holographic Entanglement Entropy in Insulator/Superconductor Transition, JHEP 1207, 088 (2012)

2012
[53]

Xiao-Mei Kuang, Eleftherios Papantonopoulos, Bin Wang, Entanglement Entropy as a Probe of the Proximity Eﬀect in Holographic Superconductors , JHEP 05, 130 (2014)

2014
[54]

Garc ´ 1a-Garc´ 1a, Conductivity and entanglement entropy of high dimensional holographic superconductors , JHEP 09, 033 (2015)

Aurelio Romero-Berm´ udez, Antonio M. Garc ´ 1a-Garc´ 1a, Conductivity and entanglement entropy of high dimensional holographic superconductors , JHEP 09, 033 (2015)

2015
[55]

Yan Peng, Qiyuan Pan, Yunqi Liu, A general holographic insulator/superconductor model awa y from the probe limit , Nucl. Phys. B 915, 69-83 (2017)

2017
[56]

Yunqi Liu, Yungui Gong, Bin Wang Non-equilibrium condensation process in holographic superconductor with nonlinear electrodynamics , JHEP 02, 116 (2016)

2016
[57]

David Dudal, Subhash Mahapatra, Interplay between the holographic QCD phase diagram and entanglement entropy , JHEP 07, 120 (2018)

2018
[58]

Fatemeh Lalehgani Dezaki, Behrouz Mirza, Marzieh Moradzade h, Zeinab Sherkatghanad, Topological invariants of the Ryu-Takayanagi (RT) surface used to observe holographic superconductor phase transition , Nuclear Physics B, 944, 114647 (2019)

2019
[59]

Hong Guo, Xiao-Mei Kuang, Bin Wang, Holographic entanglement entropy and complexity in Stuckelberg superconductor, Physics Letters B , 797, 134879 (2019). – 12 –

2019
[60]

C 44, 023101 (2020)

Yi Ling, Yuxuan Liu, Zhuo-Yu Xian, ntanglement Entropy of Annulus in Holographic Thermalization, Chinese Phys. C 44, 023101 (2020)

2020
[61]

Sunandan Gangopadhyay, Dharmesh Jain, Ashis Saha, Universal Pieces of Holographic Entanglement Entropy and Holographic Subregion Complexit y, Phys. Rev. D 102, 046002 (2020)

2020
[62]

Donald Marolf, Shannon Wang, Zhencheng Wang, Probing phase transitions of holographic entanglement entropy with ﬁxed area states , JHEP 12, 084 (2020)

2020
[63]

Araya, Robert B

Giorgos Anastasiou, Ignacio J. Araya, Robert B. Mann, Rodrig o Olea, holographic entanglement entropy in Lovelock gravity , JHEP 06, 073 (2021)

2021
[64]

Pablo Bueno, Joan Camps, Alejandro Vilar Lˇ s ®pez, Holographic entanglement entropy for perturbative higher-curvature gravities , JHEP 04, 145 (2021)

2021
[65]

Jeong, K.Y

H.S. Jeong, K.Y. Kim, and Y.W. Sun, Holographic entanglement density for spontaneous symmetry breaking, J. High Energy Phys. 06, 078 (2022)

2022
[66]

Yuanceng Xu, Yu Shi, Dong Wang, Qiyuan Pan, Holographic Entanglement Entropy and Complexity for D-Wave Superconductors , Eur. Phys. J. C 83, 202 (2023)

2023
[67]

Dong Wang, Xiongying Qiao, Mengjie Wang, Qiyuan Pan, Chuyu Lai, Jiliang Jing, Holographic entanglement entropy and subregion complexity for excited states of holographic superconductors, Nucl. Phys. B 991, 116223 (2023)

2023
[68]

Hajar Ebrahim, Monireh Ahmadpour, Holographic entanglement entropy and mutual information in deformed ﬁeld theories at ﬁnite temperature , Phys. Rev. D 107, 086010 (2023)

2023
[69]

Wanhe Zhang, Bo Yang, Weiping Yao, Holographic entanglement entropy of disk in insulator/superconductor transition with logarithmic no nlinear electrodynamics, Annals of Physics 469, 169751(2024)

2024
[70]

Yan Peng, Holographic entanglement entropy in superconductor phase transition with dark matter sector , Phys. Lett. B 750, 420-426 (2015)

2015
[71]

Strominger and C

A. Strominger and C. Vafa, Microscopic Origin of the Bekenstein-Hawking Entropy , Phys. Lett. B 379, 99 (1996)

1996
[72]

Aharony, S

O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. O z, Large N ﬁeld theories, Large N ﬁeld theories, string theory and gravity , Phys. Rept. 323, 183 (2000)

2000
[73]

Bartlomiej Kiczek, Marek Rogatko, Inﬂuence of dark matter on black hole scalar hair , Physical Review D 101, 084035 (2020)

2020
[74]

S. A. Hartnoll, C. P. Herzog, and G. T. Horowitz, Building a Holographic Superconductor , Phys. Rev. Lett. 101, 031601 (2008); S. A. Hartnoll, C. P. Herzo g, and G. T. Horowitz, Holographic Superconductors, J. High Energy Phys. 12, 015 (2008)

2008
[75]

Breitenlohner and D

P. Breitenlohner and D. Z. Freedman, Stability In Gauged Extended Supergravity , Annals Phys. 144, 249 (1982); P. Breitenlohner and D. Z. Freedman, Positive Energy In Anti-De Sitter Backgrounds And Gauged Extended Supergravity , Phys. Lett. B 115, 197 (1982)

1982
[76]

Pavan , Holographic Superconductors with various condensates in E instein-Gauss-Bonnet gravity , Phys.Rev.D 81, 106007, (2010)

Qiyuan Pan, Bin Wang, Eleftherios Papantonopoulos, Jeferson de Oliveira, A.B. Pavan , Holographic Superconductors with various condensates in E instein-Gauss-Bonnet gravity , Phys.Rev.D 81, 106007, (2010)

2010
[77]

Weiping Yao, Jiliang Jing, Holographic entanglement entropy in metal/superconducto r phase transition with exponential nonlinear electrodynamics , Phys. Lett. B 759, 533 (2016)

2016
[78]

Bardeen, L

J. Bardeen, L. N. Cooper, and J. R. Schrieﬀer, Theory of superconductivity , Phys. Rev. 108, 1175 (1957). – 13 –

1957

Pith tools

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

[1] [1]

Corbelli and P

E. Corbelli and P. Salucci, The Extended Rotation Curve and the Dark Matter Halo of M33 , Adv. Theor. Math. Phys. 2, 231-252 (1998), arXiv:astro-ph/9909252 [astro-ph]

arXiv 1998

[2] [2]

Vikhlinin, A

A. Vikhlinin, A. Kravtsov, W. Forman, C. Jones, M. Markevitch, S . S. Murray, and L. Van Speybroeck, Chandra sample of nearby relaxed galaxy clusters: mass, gas fraction, and mass-temperature relation, Astrophys. J. 640, 691 (2006), arXiv:astro-ph/0507092 [astro-ph]

arXiv 2006

[3] [3]

Clowe, M

D. Clowe, M. Bradac, A. H. Gonzalez, M. Markevitch, S. W. Randa ll, C. Jones, and D. Zaritsky, CA direct empirical proof of the existence of dark matter , Astrophys. J. 648, L109-L113 (2006), arXiv:astro-ph/0608407 [astro-ph]

arXiv 2006

[4] [5]

P. A. R. Ade, N. Aghanim, Z. Ahmed, R. W. Aikin, K. D. Alexander, M . Arnaud, J. Aumont, C. Baccigalupi, A. J. Banday et al. (BICEP2/Keck and Planck Collabor ations), Joint Analysis of BICEP2/Keck Array and Planck Data , Phys. Rev. Lett. 114, 101301 (2015), arXiv:1502.01589 [astro-ph.CO]

arXiv 2015

[5] [6]

Wagner, G

ADMX Collaboration, A. Wagner, G. Rybka, M. Hotz, L. J. Rosenb erg, S. J. Asztalos, G. Carosi et al., A Search for Hidden Sector Photons with ADMX , Phys. Rev. Lett. 105,171801 (2010)

work page 2010

[6] [7]

Horns, J

D. Horns, J. Jaeckel, A. Lindner, A. Lobanov, J. Redondo and A . Ringwald, Searching for WISPy Cold Dark Matter with a Dish Antenna , JCAP 04, 016 (2013)

work page 2013

[7] [8]

P. W. Graham, J. Mardon, S. Rajendran and Y. Zhao, Parametrically enhanced hidden photon search, Phys. Rev. D 90, 075017 (2014)

work page 2014

[8] [9]

Chaudhuri, P

S. Chaudhuri, P. W. Graham, K. Irwin, J. Mardon, S. Rajendran and Y. Zhao, Radio for hidden-photon dark matter detection , Phys. Rev. D 92, 075012 (2015)

work page 2015