Stability of Holographic Superconductors

Jiro Soda; Sugumi Kanno

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Stability of Holographic Superconductors

Sugumi Kanno, Jiro Soda

High Energy Physics - Theory · Submitted 28 Jul 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It implies the stability of the superconducting phase.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,076 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.54 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We study the dynamical stability of holographic superconductors. We first classify perturbations around black hole background solutions into vector and scalar sectors by means of a 2-dimensional rotational symmetry. We prove the stability of the vector sector by explicitly constructing the positive definite Hamiltonian. To reveal a mechanism for the stabilization of a superconducting phase, we construct a quadratic action for the scalar sector. From the action, we see the stability of black holes near a critical point is determined by the equation of motion for a charged scalar field. We show the effective mass of the charged scalar field in hairy black holes is always above the Breitenlohner-Freedman bound near the critical point due to the backreaction of a gauge field. It implies the stability of the superconducting phase. We also argue that the stability continues away from the critical point.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study the dynamical stability of holographic superconductors.	contribution 0.91	0.93	0.04	unclear 0.69
s1	We first classify perturbations around black hole background solutions into vector and scalar sectors by means of a 2-dimensional rotational symmetry.	method 0.97	0.95	0.02	asserted 0.99
s2	We prove the stability of the vector sector by explicitly constructing the positive definite Hamiltonian.	result 0.86	0.97	0.12	asserted 1.00
s3	To reveal a mechanism for the stabilization of a superconducting phase, we construct a quadratic action for the scalar sector.	method 0.78	0.96	0.04	asserted 0.92
s4	From the action, we see the stability of black holes near a critical point is determined by the equation of motion for a charged scalar field.	result 0.90	0.92	0.11	asserted 1.00
s5	We show the effective mass of the charged scalar field in hairy black holes is always above the Breitenlohner-Freedman bound near the critical point due to the backreaction of a gauge field.	result 0.99	0.93	0.30	asserted 1.00
s6	It implies the stability of the superconducting phase.	interpretation 1.00	0.80	0.50	asserted 0.65
s7	We also argue that the stability continues away from the critical point.	result 0.88	0.88	0.16	asserted 0.43

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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arXiv listing abstract v2

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full text
figures and tables
references and citing sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We study the dynamical stability of holographic superconductors. We first classify perturbations around black hole background solutions into vector and scalar sectors by means of a 2-dimensional rotational symmetry. We prove the stability of the vector sector by explicitly constructing the positive definite Hamiltonian. To reveal a mechanism for the stabilization of a superconducting phase, we construct a quadratic action for the scalar sector. From the action, we see the stability of black holes near a critical point is determined by the equation of motion for a charged scalar field. We show the effective mass of the charged scalar field in hairy black holes is always above the Breitenlohner-Freedman bound near the critical point due to the backreaction of a gauge field. It implies the stability of the superconducting phase. We also argue that the stability continues away from the critical point.

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References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Exact holographic superfluid at the Bogomolny point: transport, large charge, and R\'enyi entropies
hep-th 2026-10 accept novelty 8.0 of 10

An exact, closed-form superfluid phase exists in the probe-limit Abelian Higgs model in AdS5 at the Bogomolny coupling, yielding exact transport, large-charge scaling dimensions, and Rényi-entropy phases.
Catastrophic Instability of Small Lovelock Black Holes
gr-qc 2010-08 conditional novelty 6.0 of 10

Small Lovelock black holes are unstable in all dimensions, with tensor modes driving instability in even dimensions and scalar modes in odd dimensions.
Master Equations for Gravitational Perturbations of Static Lovelock Black Holes in Higher Dimensions
gr-qc 2010-08 accept novelty 6.0 of 10

The authors derive master equations for vector and scalar gravitational perturbations of static Lovelock black holes in any dimension, completing the full set alongside their earlier tensor result.

How the literature uses it

5 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Cites it as background 2 papers

There has been a great deal of recent work in this area, studying how the system behaves in a variety of different scenarios including altering the scalar mass and spacetime dimension, changing the gauge group and adding an external magnetic field [ref] .

The Rich Structure of Gauss-Bonnet Holographic Superconductors · Introduction · 0.99
Many aspects of holographic superconductivity are now well understood also in the $(3+1)$-dimensional case, such as their behavior in the presence of an external magnetic field, different scalar masses, potentials and backgrounds; for a (partial) list see [ref] .

Holographic Superconductors and Higher Curvature Corrections · Introduction · 0.97

What it cites · 11 sentences without a confident label

Builds on 5 papers

For example, it is possible to extend our analysis to the Gauss-Bonnet superconductors [ref] .

Holographic Superconductors with Higher Curvature Corrections · Conclusion · 0.87
For example, it is possible to extend our analysis to the Gauss-Bonnet superconductors [ref] .

Holographic Superconductors with various condensates in Einstein-Gauss-Bonnet gravity · Conclusion · 0.87
For example, it is possible to extend our analysis to the Gauss-Bonnet superconductors [ref] .

Holographic Superconductors in 3+1 dimensions away from the probe limit · Conclusion · 0.87

Uses the method or tool of 1 paper

In this section, we explain a useful method to obtain a quadratic action for black hole perturbations [ref] .

Hawking Radiation from Fluctuating Black Holes · Uses of ADM Formalism · 0.99

Cites as background 6 papers

In this section, we review the gravity/superconductor correspondence [ref] .

Building an AdS/CFT superconductor · Gravity dual of superconductors · 1.00
In this section, we review the gravity/superconductor correspondence [ref] .

Holographic Superconductors · Gravity dual of superconductors · 1.00
It is believed that the AdS/CFT correspondence is useful to study strongly coupled systems [ref] .

The Large N Limit of Superconformal Field Theories and Supergravity · Introduction · 0.99

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