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arxiv: 2606.24328 · v2 · pith:J7NHY2KHnew · submitted 2026-06-23 · ✦ hep-th

Dark-Sector Deformations of Holographic Anisotropic Superfluids in Asymptotically Hyperscaling Violation Geometry

Ji-Seong Chae This is my paper

Pith reviewed 2026-06-25 22:38 UTC · model grok-4.3

classification ✦ hep-th
keywords holographysuperfluidsdark sectorhyperscaling violationentanglement entropyanisotropyportal coupling
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The pith

Dark scalar portal weakly suppresses strip anisotropy in holographic superfluids at vanishing strength

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

The paper investigates deformations of holographic anisotropic p-wave superfluids by dark-sector portals in hyperscaling-violating black brane geometries. Visible sector fields set the chemical potential and produce anisotropic entanglement entropy for strips. Adding a kinetic portal from a dark scalar deforms the equations, and the resulting strip susceptibility at zero portal coupling is found to be negative in four and five dimensions. This indicates that the portal reduces the anisotropy induced by the visible condensate. The effect is interpreted through the holographic renormalization group, with the dark scalar affecting the infrared while narrow strips see mostly the ultraviolet boundary region.

Core claim

The main result is a strip susceptibility at vanishing portal strength. It is negative in the D=4 and D=5 backgrounds, so the portal weakly suppresses visible strip anisotropy. This has a holographic RG interpretation: the normalizable dark scalar is weighted toward the IR horizon, while narrow strips probe the UV near-boundary RT region. Thus, the portal decouples in the UV and the susceptibility vanishes quadratically with strip width.

What carries the argument

The kinetic dark-scalar portal Z_dm(Φ) which deforms the Yang-Mills operator in the visible sector.

If this is right

  • The critical shift depends on the hyperscaling-violating background and can change sign.
  • Hidden-current mixing provides a solvable example of hidden gauge sectors.
  • Isotropic dark sources cancel their contribution to the strip difference.
  • Visible quantities like critical chemical potential and condensate vary with dimension and hyperscaling exponents.

Where Pith is reading between the lines

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

  • The suppression effect might allow dark sectors to control anisotropy in holographic models of condensed matter systems.
  • Wider strips, which probe deeper into the bulk, should exhibit stronger influence from the dark sector.
  • This perturbative approach could be extended to non-perturbative regimes to check if the suppression persists.

Load-bearing premise

The dark-scalar portal can be treated as a small perturbative deformation of the visible sector without causing significant backreaction on the background geometry.

What would settle it

Computing the strip susceptibility explicitly in the D=4 case at zero portal strength and finding it positive rather than negative would falsify the suppression claim.

Figures

Figures reproduced from arXiv: 2606.24328 by Ji-Seong Chae.

Figure 1
Figure 1. Figure 1: Strip-entanglement anisotropy in D = 4 and D = 5. Panels (a) and (b) show |O(2) 12 |; panels (c) and (d) show the fractional change relative to the visible result. Case II gives the constant benchmark reduction, the isotropic mass portal lies on the visible curve, and the self-consistent kinetic portal with β = 0.8, Φh = 0.6 gives a small width-dependent suppression. The same b (Z) 0 and ωZ profiles are us… view at source ↗
Figure 2
Figure 2. Figure 2: Self-consistent tensor-portal susceptibility for the [PITH_FULL_IMAGE:figures/full_fig_p026_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Critical scale across D = 3, 4, 5. Columns correspond to the three bulk dimensions. The first two rows show the solver boundary amplitude b∞,c = √ 3 µc as a function of ϑ at z = 1 and as a function of z at ϑ = 1; the last two rows show the corresponding fractional shift, which is the same for b∞,c and µc. Case I is omitted because it coincides with the visible curve. Case II uses αdm = 0.8. The tensor port… view at source ↗
Figure 4
Figure 4. Figure 4: Self-consistent radial data at the D = 4 reference background (top row) and the D = 5 reference background (bottom row). From left to right the panels show ω1(ξ), b0(ξ), and Saniso(ξ). The visible solution is compared with the Case-II benchmark and the kinetic portal at β = 0.8, Φh = 0.6. The kinetic portal does not act as a simple multiplicative weight: both radial fields move before the source is evaluat… view at source ↗
Figure 5
Figure 5. Figure 5: Dark-minus-visible traceless source in D = 4 and D = 5. The Case-II curve is the rigid benchmark rescaling. The tensor-portal curve is the full difference Saniso[b (Z) 0 , ωZ, Z] − Saniso[b0, ω, 1], not the source-only approximation (Z − 1)S vis aniso. Its sign changes along the radial direction, which produces the partial cancellation seen in the strip susceptibility. The radial source changes appreciably… view at source ↗
Figure 6
Figure 6. Figure 6: Nonlinear condensate ⟨O⟩ 1/∆O versus µ/µc,vis in D = 3, 4, 5. Each panel compares the visible branch with Case II hidden-current mixing at αdm = 0.4 and 0.8. The vertical guide lines mark the corresponding critical shifts q 1 − α 2 dm/4, while the curves show that the source-free ordered branch follows the same displacement predicted by the linear analysis. These curves are used as consistency checks, not … view at source ↗
Figure 7
Figure 7. Figure 7: Case-II hidden-SU(2) rescaling factors controlled by αdm. The critical chemical-potential factor and the order-ϵ 2 HEE source factor follow from the same constant kinetic-mixing rescaling. The plot is kept as a benchmark rather than as the main result. 34 [PITH_FULL_IMAGE:figures/full_fig_p035_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Case-II condensate curves at the analytic reference backgrounds in [PITH_FULL_IMAGE:figures/full_fig_p036_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Case-II condensate overlay at fixed αdm = 0.8 and z = 1, with visible curves dashed and dark curves solid. Each color corresponds to a different ϑ. The hidden-sector curve associated with a given visible curve starts at lower µ/µc,vis, while the overall branch shape still reflects the visible HSV exponent [PITH_FULL_IMAGE:figures/full_fig_p037_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Case-II condensate overlay at fixed αdm = 0.8 along representative z-slices of the controlled reference backgrounds. Visible curves are dashed and dark curves are solid. The plot shows that the universal hidden-sector shift and the residual z-dependence of the visible condensate can be disentan￾gled [PITH_FULL_IMAGE:figures/full_fig_p038_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Leading strip entropy and first-law check in [PITH_FULL_IMAGE:figures/full_fig_p039_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Leading strip entropy and first-law check in [PITH_FULL_IMAGE:figures/full_fig_p040_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Leading strip entropy and first-law check in [PITH_FULL_IMAGE:figures/full_fig_p041_13.png] view at source ↗
read the original abstract

We study dark-sector deformations of holographic anisotropic \(p\)-wave superfluids in hyperscaling-violating black-brane backgrounds. In the visible \(SU(2)\) sector, \(b(u)\) fixes the chemical potential and charge density, while \(\omega(u)\) condenses and selects a boundary direction, producing anisotropic strip entanglement. The visible critical chemical potential, radial profiles, condensate branch, and strip-entanglement difference vary with dimension and hyperscaling-violating exponents. We then add hidden gauge sectors and hidden dark-scalar portals. Hidden-current mixing gives a solvable example, whereas isotropic dark sources cancel in the strip difference. For the kinetic dark-scalar portal, \(Z_{\rm dm}(\Phi)\) deforms the Yang--Mills operator; hence \(b_0(u)\), \(\omega_1(u)\), and the order-\(\epsilon^2\) anisotropic stress are computed in the same deformed problem. The critical shift depends on the hyperscaling-violating background and can change sign. The main result is a strip susceptibility at vanishing portal strength. It is negative in the \(D=4\) and \(D=5\) backgrounds, so the portal weakly suppresses visible strip anisotropy. This has a holographic RG interpretation: the normalizable dark scalar is weighted toward the IR horizon, while narrow strips probe the UV near-boundary RT region. Thus, the portal decouples in the UV and the susceptibility vanishes quadratically with strip width; wider strips reach deeper into the bulk and recover the IR dark-sector effects.

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

1 major / 0 minor

Summary. The paper studies dark-sector deformations of holographic anisotropic p-wave superfluids in hyperscaling-violating black-brane backgrounds. In the visible SU(2) sector, it examines how b(u) sets the chemical potential and charge density while ω(u) condenses to produce anisotropic strip entanglement. It then introduces hidden gauge sectors and a kinetic dark-scalar portal Z_dm(Φ) that deforms the Yang-Mills operator. The central result is the strip susceptibility at vanishing portal strength ε, which is negative for D=4 and D=5 backgrounds, implying that the portal weakly suppresses visible strip anisotropy. The analysis includes dependence on dimension and hyperscaling exponents, plus a holographic RG interpretation linking the IR-weighted normalizable dark scalar to UV decoupling for narrow strips.

Significance. If the central claim holds, the work provides a concrete holographic example of how a perturbative dark-sector portal can modulate visible-sector observables such as strip entanglement anisotropy, with an explicit RG interpretation of UV/IR decoupling. The sign change of the susceptibility with background parameters and the cancellation properties for isotropic sources are potentially useful for model-building in holographic dark-sector scenarios.

major comments (1)
  1. [Abstract] Abstract and the paragraph describing the kinetic portal: the central claim (negative strip susceptibility at vanishing portal strength) is obtained by solving the deformed equations for b0(u), ω1(u) and the O(ε²) anisotropic stress while treating the hyperscaling-violating black-brane geometry as fixed. No explicit check is given that the stress-energy of the normalizable dark scalar induces only O(ε²) corrections to the radial warp factor or blackening function; if backreaction enters at O(ε), both the extracted susceptibility and its reported sign become unreliable. This assumption is load-bearing for the main result.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and the constructive comment on the backreaction of the normalizable dark scalar. We address the concern below and will revise the manuscript to strengthen the presentation of this point.

read point-by-point responses

  1. Referee: [Abstract] Abstract and the paragraph describing the kinetic portal: the central claim (negative strip susceptibility at vanishing portal strength) is obtained by solving the deformed equations for b0(u), ω1(u) and the O(ε^{2}) anisotropic stress while treating the hyperscaling-violating black-brane geometry as fixed. No explicit check is given that the stress-energy of the normalizable dark scalar induces only O(ε^{2}) corrections to the radial warp factor or blackening function; if backreaction enters at O(ε), both the extracted susceptibility and its reported sign become unreliable. This assumption is load-bearing for the main result.

    Authors: We agree that an explicit verification of the backreaction order is necessary to confirm the reliability of the susceptibility and its sign. The current analysis solves the deformed visible-sector equations on the fixed hyperscaling-violating background, which is the standard probe approximation for such portal deformations. The normalizable dark scalar is IR-weighted, which already suggests suppression of its stress-energy contribution near the boundary (relevant for narrow strips). To address the referee's point directly, we will add a new appendix that computes the leading O(ε^{2}) corrections to the metric functions induced by the dark scalar's stress-energy tensor and verifies that these corrections do not modify the O(ε^{2}) anisotropic stress or the extracted susceptibility at leading order for the D=4 and D=5 backgrounds. This will explicitly confirm that backreaction remains subleading and does not affect the reported sign. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is a direct perturbative computation within the model

full rationale

The paper computes the strip susceptibility by explicitly solving the deformed Yang-Mills equations with the Z_dm(Phi) portal term for b0(u), omega1(u) and the O(epsilon^2) stress tensor in the fixed hyperscaling-violating background. This is a standard holographic calculation of a derived quantity from the bulk equations rather than a self-definitional loop, a fitted parameter renamed as prediction, or a load-bearing self-citation. No uniqueness theorem or ansatz is imported from prior author work in the provided text, and the result is not equivalent to its inputs by construction. The model is self-contained as a theoretical derivation without external data fitting.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on the standard holographic dictionary, the existence of a hyperscaling-violating black-brane solution, and the perturbative treatment of the portal; no independent evidence is given for any of these within the abstract.

free parameters (2)
  • hyperscaling-violating exponents
    Define the background geometry and are varied to obtain the D=4,5 results; their values are inputs rather than derived.
  • portal coupling strength epsilon
    Expanded to second order; the susceptibility is the coefficient of the linear term in epsilon.
axioms (2)
  • domain assumption Einstein-Yang-Mills equations admit hyperscaling-violating black-brane solutions with the stated asymptotics
    Invoked to set up the visible-sector background before the portal is added.
  • ad hoc to paper The dark scalar is normalizable and does not back-react at leading order
    Required for the perturbative expansion of b0(u) and omega1(u).
invented entities (1)
  • kinetic dark-scalar portal Z_dm(Phi) no independent evidence
    purpose: Deforms the visible Yang-Mills kinetic term to couple hidden and visible sectors
    Postulated to generate the deformation; no independent evidence supplied.

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