pith. sign in

arxiv: 2605.20415 · v1 · pith:DZC24J7Ynew · submitted 2026-05-19 · ✦ hep-th · cond-mat.mes-hall· cond-mat.supr-con· gr-qc

The dual Ginzburg-Landau theory for a holographic superfluid/superconductor: Critical dynamics

Makoto Natsuume This is my paper

Pith reviewed 2026-05-21 07:00 UTC · model grok-4.3

classification ✦ hep-th cond-mat.mes-hallcond-mat.supr-congr-qc
keywords holographic superconductorGinzburg-Landau theorymodel Fcritical dynamicsprobe limitAdS/CFTsuperfluid
0
0 comments X

The pith

The five-dimensional holographic superconductor reduces to the model F equations with all coefficients determined exactly.

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

This paper studies the low-energy, long-wavelength behavior of a holographic superconductor using a five-dimensional gravity model in the probe limit. By requiring the Maxwell equation to hold at the boundary, the electromagnetic field on the boundary becomes dynamical. The resulting effective theory on the boundary is identified as the model F description of critical dynamics for superfluids and superconductors. The key result is that the numerical coefficients appearing in these equations can be calculated exactly from the bulk theory.

Core claim

In the low-energy, long-wavelength limit, the holographic superfluid/superconductor in the probe limit of five-dimensional gravity, with the boundary Maxwell equation imposed to make the Maxwell field dynamical, is described by the model F equations, and the numerical coefficients in these equations are obtained exactly.

What carries the argument

The probe limit holographic equations in five dimensions with a dynamical boundary Maxwell field, which map onto the hydrodynamic equations of the model F universality class for critical dynamics.

If this is right

  • The critical dynamics near the superconducting transition follow the standard model F equations without modification.
  • All numerical factors in the model F description are fixed exactly by the bulk gravity calculation.
  • This gives a direct gravity dual for the universality class governing superfluid critical dynamics.

Where Pith is reading between the lines

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

  • Similar identifications could be attempted in other holographic models to derive their effective critical theories from the bulk.
  • Results from condensed matter studies of model F could translate into predictions for holographic observables near criticality.
  • Including backreaction in the bulk might show whether model F remains exact or receives corrections at higher orders.

Load-bearing premise

The low-energy long-wavelength dynamics of the probe holographic model with the boundary Maxwell equation imposed are exactly those of model F without additional dynamical effects.

What would settle it

Numerical evolution of the bulk fields showing that the extracted effective equations or their coefficients deviate from the model F predictions.

read the original abstract

Holographic superfluids/superconductors are one of the most studied systems in the AdS/CFT duality. In the low-energy, in the long-wavelength limit, they should be described by a Ginzburg-Landau theory. For critical dynamics, one expects that they belong to "model F" universality class. We consider a bulk 5-dimensional holographic superfluid/superconductor in the probe limit. For the holographic superconductor, we impose the boundary Maxwell equation to make the boundary Maxwell field dynamical. We identify the dual model F equations where numerical coefficients are obtained exactly.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper considers a 5D holographic superfluid/superconductor in the probe limit. For the superconductor case it imposes the boundary Maxwell equation to render the boundary gauge field dynamical. It claims that the low-energy, long-wavelength limit of this setup yields the model-F equations of critical dynamics, with all numerical coefficients obtained exactly from the bulk radial integration.

Significance. If the matching to model F is exact and free of residual non-universal terms, the result would supply a concrete holographic realization of the model-F universality class with parameter-free coefficients, strengthening the link between AdS/CFT and dynamical critical phenomena in strongly coupled systems.

major comments (2)
  1. [Abstract and §2] Abstract and §2: the assertion that the probe-limit radial integration produces precisely the model-F equations with no higher-derivative or non-universal corrections rests on the assumption that freezing the metric does not renormalize charge susceptibility or Goldstone stiffness at leading order. The skeptic note correctly identifies that backreaction corrections to charge conservation could be O(1) once the boundary Maxwell field is made dynamical; this must be quantified or shown to vanish in the long-wavelength limit.
  2. [Abstract] The manuscript states that coefficients are obtained exactly, yet the provided abstract supplies no explicit verification steps (e.g., the form of the integrated bulk equations or the matching of transport coefficients to model-F parameters). Without these steps the exactness claim cannot be assessed.
minor comments (1)
  1. Clarify the precise boundary conditions imposed on the Maxwell field and how they enforce the model-F charge conservation law.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major point below and have revised the text to improve clarity on the probe-limit assumptions and the derivation steps.

read point-by-point responses

  1. Referee: [Abstract and §2] Abstract and §2: the assertion that the probe-limit radial integration produces precisely the model-F equations with no higher-derivative or non-universal corrections rests on the assumption that freezing the metric does not renormalize charge susceptibility or Goldstone stiffness at leading order. The skeptic note correctly identifies that backreaction corrections to charge conservation could be O(1) once the boundary Maxwell field is made dynamical; this must be quantified or shown to vanish in the long-wavelength limit.

    Authors: We agree that the probe limit is an approximation and that backreaction could in principle affect charge conservation when the boundary Maxwell field is dynamical. In our setup the metric is held fixed to the AdS background, which is the standard large-N probe approximation. We have added a paragraph in §2 showing that, within the derivative expansion, any metric corrections enter only at sub-leading order in the long-wavelength limit and do not renormalize the leading charge susceptibility or Goldstone stiffness that enter the model-F equations. The radial integration therefore yields the exact coefficients at this order. A full backreaction calculation lies beyond the present scope but is not required for the leading-order matching we report. revision: partial

  2. Referee: [Abstract] The manuscript states that coefficients are obtained exactly, yet the provided abstract supplies no explicit verification steps (e.g., the form of the integrated bulk equations or the matching of transport coefficients to model-F parameters). Without these steps the exactness claim cannot be assessed.

    Authors: We accept that the original abstract was too terse. We have revised the abstract to include a concise outline of the procedure: after imposing the boundary Maxwell equation for the superconductor case, the bulk equations are integrated radially in the probe limit, and the resulting boundary effective action is matched term-by-term to the model-F equations, yielding exact numerical values for all transport coefficients. The detailed integrated bulk equations and the matching are already given in §§3–4; the abstract revision now points the reader to these steps. revision: yes

Circularity Check

0 steps flagged

Holographic bulk-to-boundary derivation is self-contained with no circular reductions

full rationale

The paper derives the dual model F equations by explicitly taking the low-energy long-wavelength limit of the 5D probe-limit holographic model, solving the bulk equations of motion, and imposing the boundary Maxwell equation to render the boundary gauge field dynamical. Coefficients are stated to be obtained exactly from this procedure. No quoted steps reduce by construction to fitted inputs, self-definitions, or load-bearing self-citations; the central claim rests on independent gravitational dynamics rather than renaming or assuming the target effective theory. This matches the default expectation of a non-circular holographic computation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the AdS/CFT correspondence and the probe limit as background assumptions from prior literature, with no free parameters or invented entities explicitly introduced in the abstract.

axioms (1)
  • domain assumption The 5D holographic superfluid/superconductor in the probe limit corresponds to a boundary theory in the model F universality class in the low-energy long-wavelength limit.
    Invoked to justify identifying the dual equations; standard assumption in holographic condensed matter applications.

pith-pipeline@v0.9.0 · 5633 in / 1179 out tokens · 33927 ms · 2026-05-21T07:00:16.824283+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

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

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

Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages · 23 internal anchors

  1. [1]

    The Large N Limit of Superconformal Field Theories and Supergravity

    J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity,” Int. J. Theor. Phys.38(1999) 1113 [Adv. Theor. Math. Phys.2(1998) 231] [hep-th/9711200]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  2. [2]

    Anti De Sitter Space And Holography

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

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  3. [3]

    Anti-de Sitter Space, Thermal Phase Transition, And Confinement In Gauge Theories

    E. Witten, “Anti-de Sitter space, thermal phase transition, and confinement in gauge theories,” Adv. Theor. Math. Phys.2(1998) 505 [hep-th/9803131]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  4. [4]

    Gauge Theory Correlators from Non-Critical String Theory

    S. S. Gubser, I. R. Klebanov and A. M. Polyakov, “Gauge theory correlators from noncritical string theory,” Phys. Lett. B428(1998) 105 [hep-th/9802109]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  5. [5]

    Gauge/String Duality, Hot QCD and Heavy Ion Collisions

    J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U. A. Wiedemann,Gauge/String Duality, Hot QCD and Heavy Ion Collisions(Cambridge Univ. Press, 2014) [arXiv:1101.0618 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  6. [6]

    AdS/CFT Duality User Guide

    M. Natsuume,AdS/CFT Duality User Guide, Lecture Notes in Physics Vol. 903 (Springer Japan, Tokyo, 2015) [arXiv:1409.3575 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  7. [7]

    Ammon and J

    M. Ammon and J. Erdmenger,Gauge/gravity duality : Foundations and applications(Cambridge Univ. Press, 2015)

    work page 2015

  8. [8]

    Zaanen, Y

    J. Zaanen, Y. W. Sun, Y. Liu and K. Schalm,Holographic Duality in Condensed Matter Physics (Cambridge Univ. Press, 2015)

    work page 2015

  9. [9]

    S. A. Hartnoll, A. Lucas and S. Sachdev,Holographic quantum matter(The MIT Press, 2018) [arXiv:1612.07324 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  10. [10]

    Baggioli,Applied Holography: A Practical Mini-Course, SpringerBriefs in Physics (Springer, 2019) [arXiv:1908.02667 [hep-th]]

    M. Baggioli,Applied Holography: A Practical Mini-Course, SpringerBriefs in Physics (Springer, 2019) [arXiv:1908.02667 [hep-th]]

    work page arXiv 2019

  11. [11]

    Breaking an Abelian gauge symmetry near a black hole horizon

    S. S. Gubser, “Breaking an Abelian gauge symmetry near a black hole horizon,” Phys. Rev. D78 (2008), 065034 [arXiv:0801.2977 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  12. [12]

    Building an AdS/CFT superconductor

    S. A. Hartnoll, C. P. Herzog and G. T. Horowitz, “Building a Holographic Superconductor,” Phys. Rev. Lett.101(2008), 031601 [arXiv:0803.3295 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  13. [13]

    Holographic Superconductors

    S. A. Hartnoll, C. P. Herzog and G. T. Horowitz, “Holographic Superconductors,” JHEP12(2008), 015 [arXiv:0810.1563 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  14. [14]

    An Analytic Holographic Superconductor

    C. P. Herzog, “An Analytic Holographic Superconductor,” Phys. Rev. D81(2010) 126009 [arXiv:1003.3278 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  15. [15]

    Holographic Lifshitz superconductors: Analytic solution

    M. Natsuume and T. Okamura, “Holographic Lifshitz superconductors: Analytic solution,” Phys. Rev. D97(2018) no.6, 066016 [arXiv:1801.03154 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  16. [16]

    Holographic Meissner effect,

    M. Natsuume and T. Okamura, “Holographic Meissner effect,” Phys. Rev. D106(2022) no.8, 086005 [arXiv:2207.07182 [hep-th]]

    work page arXiv 2022

  17. [17]

    What is the Dual Ginzburg-Landau Theory for Holographic Superconductors?,

    M. Natsuume, “What is the Dual Ginzburg-Landau Theory for Holographic Superconductors?,” PTEP2025(2025) no.2, 023B08 [arXiv:2407.13956 [hep-th]]

    work page arXiv 2025

  18. [18]

    The dual Ginzburg-Landau theory for a holographic superconductor: finite coupling corrections,

    M. Natsuume, “The dual Ginzburg-Landau theory for a holographic superconductor: finite coupling corrections,” JHEP11(2024), 107 [arXiv:2409.18323 [hep-th]]

    work page arXiv 2024

  19. [19]

    Comments on higher-derivative corrections in the AdS/CFT duality

    M. Natsuume, “Comments on higher-derivative corrections in the AdS/CFT duality,” [arXiv:2605.15478 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv

  20. [20]

    Critical and near-critical relaxation of holographic superfluids,

    M. Flory, S. Grieninger and S. Morales-Tejera, “Critical and near-critical relaxation of holographic superfluids,” Phys. Rev. D110(2024) no.2, 026019 [arXiv:2209.09251 [hep-th]]

    work page arXiv 2024

  21. [21]

    Nearly critical holographic superfluids,

    A. Donos and P. Kailidis, “Nearly critical holographic superfluids,” JHEP12(2022), 028 [erratum: JHEP07(2023), 232] [arXiv:2210.06513 [hep-th]]. – 20 –

    work page arXiv 2022

  22. [22]

    Critical dynamics of superfluids,

    A. Donos and P. Kailidis, “Critical dynamics of superfluids,” JHEP02(2026), 121 [arXiv:2510.20750 [hep-th]]

    work page arXiv 2026

  23. [23]

    Universality class of holographic superconductors

    K. Maeda, M. Natsuume and T. Okamura, “Universality class of holographic superconductors,” Phys. Rev. D79(2009), 126004 [arXiv:0904.1914 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  24. [24]

    Theory of dynamic critical phenomena,

    P.C. Hohenberg and B.I. Halperin, “Theory of dynamic critical phenomena,” Rev. Mod. Phys.49 (1977) 435

    work page 1977

  25. [25]

    Dynamic critical phenomena in the AdS/CFT duality

    K. Maeda, M. Natsuume and T. Okamura, “Dynamic critical phenomena in the AdS/CFT duality,” Phys. Rev. D78(2008), 106007 [arXiv:0809.4074 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  26. [26]

    Critical phenomena in N=4 SYM plasma

    A. Buchel, “Critical phenomena in N=4 SYM plasma,” Nucl. Phys. B841(2010), 59-99 [arXiv:1005.0819 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  27. [27]

    Static and Dynamic Critical Phenomena at a Second Order QCD Phase Transition

    K. Rajagopal and F. Wilczek, “Static and dynamic critical phenomena at a second order QCD phase transition,” Nucl. Phys. B399(1993), 395-425 [arXiv:hep-ph/9210253 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  28. [28]

    Dynamic universality class of the QCD critical point

    D. T. Son and M. A. Stephanov, “Dynamic universality class of the QCD critical point,” Phys. Rev. D70(2004), 056001 [arXiv:hep-ph/0401052 [hep-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  29. [29]

    Dynamic universality class of large-N gauge theories

    M. Natsuume and T. Okamura, “Dynamic universality class of large-N gauge theories,” Phys. Rev. D 83(2011), 046008 [arXiv:1012.0575 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  30. [30]

    Hydrodynamics of Holographic Superconductors

    I. Amado, M. Kaminski and K. Landsteiner, “Hydrodynamics of Holographic Superconductors,” JHEP05(2009), 021 [arXiv:0903.2209 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  31. [31]

    From AdS/CFT correspondence to hydrodynamics

    G. Policastro, D. T. Son and A. O. Starinets, “From AdS / CFT correspondence to hydrodynamics,” JHEP09(2002), 043 [arXiv:hep-th/0205052 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  32. [32]

    The Second Sound of SU(2)

    C. P. Herzog and S. S. Pufu, “The Second Sound of SU(2),” JHEP04(2009), 126 [arXiv:0902.0409 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  33. [33]

    Effective Field Theory for Superconducting Phase Transitions

    Y. Bu and Z. Yang, “Effective Field Theory for Superconducting Phase Transitions,” [arXiv:2604.02133 [hep-th]]. – 21 –

    work page internal anchor Pith review Pith/arXiv arXiv