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REVIEW 2 major objections 4 minor 1 cited by

Disorder changes the infrared fate of holographic metals in opposite ways depending on dimension: in AdS4 it leaves a finite residual resistivity, in AdS3 it is washed out and the clean fixed point is restored.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-04 21:10 UTC pith:XS7C33GC

load-bearing objection Fully backreacted disordered charged horizons are genuinely new and the numerics look credible, but the AdS4 'finite residual resistivity at T=0' is an extrapolation across the IR cutoff and should be framed as such. the 2 major comments →

arxiv 2509.08164 v1 pith:XS7C33GC submitted 2025-09-09 hep-th cond-mat.str-elgr-qc

Disordered Charged Horizons

Daniel Arean , Sebastian Grieninger , Pau G. Romeu This is my paper
classification hep-th cond-mat.str-elgr-qc
keywords holographic disordercharged black branesresidual resistivityHarris criterionAdS/CFT correspondenceDC transportquantum critical pointinhomogeneous horizons
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper constructs fully backreacted black brane solutions whose boundary chemical potential is a random function of position, in both AdS4 (a 2+1-dimensional dual) and AdS3 (1+1 dimensions). At intermediate temperatures the horizons are strongly wavy, but their spatial averages reproduce the clean Reissner-Nordstrom and BTZ geometries. The low-temperature story splits: in AdS4 the averaged geometry flows to the clean AdS2 x R^2 throat while the actual horizon stays disordered, and the DC resistivity settles to a finite value; in AdS3 the waviness decays and the horizon returns to the clean charged BTZ fixed point, so conductivity grows without bound as T goes to 0. The paper takes this dimension-dependent fate as evidence that the Harris criterion, a perturbative rule of thumb about when disorder matters, does not reliably describe strongly coupled systems.

Core claim

The central claim is that an inhomogeneous chemical potential that is Harris-relevant in both dimensions still has opposite infrared fates depending on spacetime dimension. In AdS4 the near-horizon geometry remains modulated at the lowest accessible temperatures; the averaged invariants match the clean AdS2 x R^2 throat, but the horizon's distortion along the homogeneous direction, measured by the norm W and the term <Upsilon^2>, does not vanish. This persistent inhomogeneity keeps the denominator of the horizon formula for the DC conductivity finite, giving a finite residual resistivity and a thermoelectric coefficient alpha that also saturates while kappa goes to zero linearly. In AdS3, by

What carries the argument

The load-bearing object is the disordered source mu(x) = mu0 [1 + (w/N) sum_n cos(n k0/N x + delta_n)], a sum of N cosines with random phases that reproduces local white noise with strength V when N goes to infinity. The argument is carried by the near-horizon analysis of the resulting Einstein-Maxwell solutions: transport coefficients are written as horizon integrals, with sigma = (1/Z)[1 + <rho>^2/(<rho^2> - <rho>^2 + <Upsilon^2>)] in AdS4 and sigma = (1/Z)[1 + <rho>^2/(<rho^2> - <rho>^2)] in AdS3, so the denominators measure exactly how much the horizon electric field and geometry vary. If a denominator tends to zero the clean divergent conductivity is recovered; the paper's numerical cla

Load-bearing premise

The zero-temperature conclusions come from extrapolating finite-temperature solutions across an infrared cutoff, not from computing the disordered ground state: if the 1/log T resistivity regime conceded in the paper's own footnote sets in below that window, or if the single-cosine zero-temperature solutions do not represent the full multi-cosine ensemble, the dimension-dependence story would need revision.

What would settle it

Run the AdS4 construction at temperatures below kIR = k0/N (by raising N at fixed k0) and measure rho_DC: a flat plateau confirms the residual resistivity, a 1/log T rise refutes it; likewise, solve the zero-temperature equations with a genuinely multi-cosine disordered source and check whether the horizon stays modulated, since the single-cosine solutions of Appendix B are the current evidence for persistence.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • In a 2+1-dimensional strongly coupled metal with Harris-relevant charge disorder, the DC resistivity does not vanish at zero temperature; each realization fails to reach the clean quantum critical point even though the averaged geometry looks like it does.
  • In 1+1 dimensions, disorder is an irrelevant deformation: the horizon returns to the clean AdS2 x R geometry and electrical conductivity diverges as T goes to 0, so translation invariance is effectively restored in the infrared.
  • The averaged geometry is not itself a solution of Einstein's equations; disorder leaves a macroscopic imprint as an effective graviton mass M_g^2 ~ <rho^2> - <rho>^2 + <Upsilon^2>, which gives homogeneous massive-gravity models a concrete interpretation as coarse-grained versions of these disordered solutions.
  • The standard Harris criterion fails for these strongly coupled holographic systems: Harris-relevant disorder can behave as a marginal deformation in AdS4 or as an irrelevant one in AdS3.
  • In the AdS4 disordered metal the thermal conductivity vanishes linearly with temperature while sigma and alpha saturate, a distinctive signature of the persistent inhomogeneous horizon.

Where Pith is reading between the lines

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

  • If the residual-resistivity plateau is real, a direct extension is to compute AC or optical conductivity in these disordered backgrounds: it should show a dissipation feature whose width tracks the effective graviton mass, whereas the clean AdS2 throat would show no such peak.
  • The strict zero-temperature conclusion rests on an extrapolation; the paper's own footnote concedes a 1/log T resistivity regime at exponentially low temperatures. If that regime is realized, 'residual resistivity' would become a slow logarithmic decay rather than a constant, softening but not erasing the dimensional contrast.
  • The near-horizon scaling-dimension template (marginal in AdS4, irrelevant in AdS3) could be applied to higher-dimensional charged black branes to test whether the dimension-dependence persists in AdS5 and beyond; the paper leaves this open.
  • Because the averaged low-temperature theory looks like a line of critical points labeled by disorder strength, disorder-averaged two-point functions may differ from the clean AdS2 fixed-point correlators; computing them would reveal whether the disordered ensemble defines a genuinely new fixed point.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper constructs fully backreacted Einstein-Maxwell black brane solutions with a spatially disordered chemical potential (2.3) in asymptotically AdS4 and AdS3, using the DeTurck method. At intermediate temperatures the horizons are strongly inhomogeneous while geometric averages reproduce the clean Reissner-Nordström and BTZ solutions. The main physical claims are dimensional dichotomy: in AdS4 the horizon inhomogeneities persist at low temperature and the DC conductivity flattens, indicating a finite residual resistivity at T→0, whereas in AdS3 the inhomogeneities decay and the conductivity grows as a power law, signaling restoration of the clean AdS2×R IR fixed point. The paper interprets this as disorder qualitatively changing the IR physics of holographic metals and as evidence for Harris-criterion violations in strongly coupled systems.

Significance. If the T→0 claims are correct, this is a significant step beyond perturbative and probe-limit treatments of holographic disorder: it provides fully backreacted, explicit disordered charged horizons in two and three bulk dimensions and derives DC transport from horizon data without fitting parameters. The numerics are credible: the DeTurck vector decays exponentially with resolution (Fig. 22), global averages change by less than 0.05% under refinement, and the AdS3 conclusion has independent analytic support from the scaling dimension in eq. (5.1). The transport formulas (3.20) and (3.28) are derived from the established Donos–Gauntlett horizon procedure. However, the central AdS4 statement of a finite residual resistivity at strictly T=0 is an extrapolation across the infrared cutoff (2.7) and is not directly computed; the load-bearing zero-temperature evidence in Appendix B uses single-mode modulated solutions. The paper's value is therefore presently more in the construction and intermediate-temperature phenomenology than in the strict zero-temperature claim.

major comments (2)
  1. [§4.2, Fig. 9, footnote 6; Abstract] The claim of a finite residual resistivity at T=0 is not established. The numerics are confined to the disordered window (2.7), T/μ0 > kIR/μ0 = k0/(N μ0), i.e. T/μ0 ≳ 5×10^-4 for the main runs. Within the window ρ_DC flattens and its log-derivative is 'consistent with zero' (Fig. 9), but no error bars, realization spread, or N-dependence of the plateau are shown, so slow logarithmic decay is not excluded. The paper's own eq. (4.6) gives Δ ≈ 1 + k̂^4/2, and footnote 6 concedes a 1/log T regime at exponentially low T below the window, in which ρ_DC → 0. Thus the abstract's 'finite residual resistivity' is an extrapolation across (2.7), not a computation. Please either soften the T=0 wording or provide evidence that the 1/log T regime is avoided for the multi-mode ensemble.
  2. [Appendix B, §4.1] The zero-temperature support for persistent inhomogeneity uses single-mode modulated solutions (B.1) with k/μ0 = 0.075 and 0.025, while the disordered source (2.3) with N=40 and k0/μ0=0.08 contains modes down to k/μ0 = 0.002 and multi-mode mixing. Since the IR scaling dimension (4.6) is k-dependent (Δ ≈ 1 + k̂^4/2), the most marginal modes are precisely the ones absent from the single-mode extremal construction. Thus extremality of a single cosine does not establish extremality of the full disorder profile; Fig. 14 is a finite-temperature N-convergence check, not a T→0 check. Please either construct zero-temperature multi-mode solutions or justify that the single-mode behavior is representative in the T→0 limit.
minor comments (4)
  1. [Section 6, eq. (2.3)] The Conclusions state that the disorder sum contains wavevectors k_n = k0/n, but eq. (2.3) defines k_n = n k0/N. Please correct this typo.
  2. [Fig. 10 right, §4.2] The caption of the right panel of Fig. 10 says the overall factor Z 'remains below one', while the main text states that 'Z is above one for all temperatures and disorder strengths'. These are opposite statements and must be reconciled.
  3. [§4.1 (Fig. 19)] In the discussion of Fig. 19, the phrase 'similarly to the disordered case in Fig. 19' appears to refer to Fig. 5, not Fig. 19 itself. Please fix the reference.
  4. [Footnote 6] For clarity, footnote 6 should explicitly tie the 1/log T prediction to the deformation analysis of eq. (4.6) and state the dimensionless condition T/μ0 ∼ e^{-1/kIR} in terms of the mode k̂, since this is the basis for the caveat on the residual resistivity.

Circularity Check

0 steps flagged

No significant circularity: the paper's central claims are outputs of a PDE construction; cited self-works are not load-bearing.

full rationale

I walked the derivation chain: the disordered chemical potential (2.3) is an input; the fully backreacted AdS3 and AdS4 geometries are obtained by solving the Einstein-Maxwell equations with DeTurck gauge fixing; the DC thermoelectric conductivities (3.20) and (3.28) are derived from the established Donos-Gauntlett horizon-data formalism rather than fitted to a target observable; and the IR scaling dimensions (4.6) and (5.1) are perturbative computations about the clean IR geometry, independent of the numerical low-temperature results. The residual resistivity in AdS4 is an emergent property of the nonvanishing horizon-data denominator (⟨ρ^2⟩−⟨ρ⟩^2+⟨Υ^2⟩), not a parameter fitted to the resistivity itself. The AdS3 result follows from the same transport formulas plus the observed power-law decay of horizon inhomogeneities. No step defines a prediction in terms of the quantity being predicted, and no load-bearing claim is supported solely by a self-citation. The self-citations [17,29,46] are historical or technical (disorder implementation, finite-N delta-function avatar, future superconductor directions) and do not carry the central derivation. The manuscript itself flags the main limitation: footnote 6 concedes that a 1/log T resistivity regime predicted in [40] would set in at exponentially low temperatures below the window (2.7), so the strict T→0 residual resistivity is an extrapolation across the IR cutoff; likewise, Appendix B's single-cosine extremal solutions are a supporting consistency check rather than a proof of the full multi-cosine disordered limit. These are extrapolation and completeness concerns, not circularity. The derivation is self-contained against the external Donos-Gauntlett transport framework and the independent perturbative IR scaling analysis.

Axiom & Free-Parameter Ledger

3 free parameters · 7 axioms · 1 invented entities

The paper's central claims rest on no fitted parameters: the disorder amplitude w, UV cutoff k0/mu0, and mode number N are inputs scanned over ranges, and the residual resistivity, geometric averages, and dimensional dichotomy are emergent from numerically solving the Einstein-Maxwell PDEs. The main axioms are the Einstein-Maxwell bulk action, the finite-mode representation (2.3) of white-noise disorder, the DeTurck trick's validity (checked numerically via xi^2), and the Donos-Gauntlett horizon-data transport formulas. The load-bearing axiom is that behavior inside the disordered temperature window (2.7) determines the exact T to 0 limit; this is an ad hoc-to-paper assumption flagged by the authors themselves (footnote 6). No invented entities are introduced.

free parameters (3)
  • Disorder amplitude w and disorder strength V/sqrt(mu0) = w in [0.004, 0.02] giving V/sqrt(mu0) in [0.25, 1.25] (AdS4); V/sqrt(mu0) in [0.2, 1] (AdS3)
    Input source amplitude in (2.3); the residual resistivity and the line of IR critical points are demonstrated for these values; no observable is fitted to set w.
  • UV cutoff k0/mu0 = 0.06 to 0.08 (AdS4), about 1 (AdS3)
    Sets the disorder temperature window (2.7); kept fixed while temperature is varied; the paper argues (Fig. 14) that results are insensitive to it within the disordered regime.
  • Mode number N (IR cutoff kIR = k0/N) = N = 40 (AdS4), N = 6 to 20 (AdS3, see Fig. 22)
    Finite-N truncation of (2.3); convergence in N is checked (Figs. 14, 22), but the exact N to infinity white-noise limit is not reached numerically.
axioms (7)
  • domain assumption Einstein-Maxwell action (3.1) is the complete bulk description of the disordered duals
    The holographic model; IR claims (residual resistivity, dimensional dichotomy) are specific to this theory, as the paper itself notes when discussing extensions (Section 6).
  • domain assumption Finite-mode profile (2.3) with uniformly drawn phases represents quenched white-noise disorder; disorder averages via (2.4)
    Standard representation from [13,17,18,29]; the identification with a delta function (2.5) is only valid for modes below k0 and for system size 2 pi N/k0 (Section 2).
  • standard math Solutions of the Einstein-DeTurck equations with vanishing DeTurck vector are genuine Einstein solutions
    Numerically verified via xi^2 < 10^-4 and exponential decay of xi^2 with resolution (Appendix C.2, Fig. 22); a general proof is not available per [35].
  • domain assumption Donos-Gauntlett horizon-data formalism (3.10)-(3.15) yields the DC thermoelectric conductivities
    Standard method for inhomogeneous holographic geometries [30,36,37]; corrections from DeTurck-ing are O(xi^2) per footnote 3.
  • ad hoc to paper The T to 0 limit is determined by behavior inside the disordered temperature window (2.7)
    Load-bearing for the residual-resistivity and disorder-relevance claims; footnote 6 concedes a possible 1/log T regime below the window.
  • standard math Harris criterion (2.1) with current operator dimension Delta_J = d-1
    Used to classify disorder as Harris-relevant; the paper argues its failure is the headline result (Section 2, Conclusions).
  • domain assumption Near-horizon perturbation analysis about the clean IR geometry governs the fate of disorder
    Eqs. (4.6), (5.1) follow [40] and assume the disordered solutions are small deformations of the clean throat in the IR (Sections 4.1.1, 5.1.1).
invented entities (1)
  • None no independent evidence
    purpose: No new particle, mediator, force, dimension, or conserved quantity is introduced
    The effective graviton mass M_g^2 in eq. (4.7) is an interpretation borrowed from massive gravity [41,42], and the disorder strength V is a physical input, not a new entity.

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Cite this review

Pith. "Pith review of Disordered Charged Horizons." pith.science (2026). https://pith.science/paper/XS7C33GC

@misc{pith2026250908164,
  author       = {Pith},
  title        = {Pith review of: Disordered Charged Horizons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XS7C33GC}},
  note         = {Machine review of arXiv:2509.08164}
}
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read the original abstract

We construct fully backreacted charged black brane solutions with a spatially disordered chemical potential in asymptotically AdS$_3$ and AdS$_4$, providing holographic duals of strongly coupled disordered systems. At intermediate temperatures these geometries display highly inhomogeneous horizons, though their geometric averages reproduce the clean BTZ and Reissner-Nordstr\"om solutions. The low temperature behavior, however, differs sharply between dimensions. In AdS$_3$, inhomogeneities decay and the horizon flows to the clean charged BTZ fixed point, rendering disorder irrelevant in the infrared. In AdS$_4$, horizon inhomogeneities persist: while the averaged geometry flows to the clean AdS$_2\times \mathbb{R}^2$ throat, the disordered horizon induces a finite residual resistivity. These results show that disorder can qualitatively alter the IR physics of holographic metals and indicate violations of the Harris criterion in strongly coupled systems.

discussion (0)

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.