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The Rich Structure of Gauss-Bonnet Holographic Superconductors
High Energy Physics - Theory · Submitted 14 Dec 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that when the mass approaches the Breitenlohner-Freedman (BF) bound and $\alpha\rightarrow L^2/4$ the effect of backreaction is to increase the critical temperature, $T_c$, of the system: the opposite of its effect in the rest of parameter space.
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The abstract, sentence by sentence
We study fully backreacting, Gauss-Bonnet (GB) holographic superconductors in 5 bulk spacetime dimensions. We explore the system's dependence on the scalar mass for both positive and negative GB coupling, $\alpha$. We find that when the mass approaches the Breitenlohner-Freedman (BF) bound and $\alpha\rightarrow L^2/4$ the effect of backreaction is to increase the critical temperature, $T_c$, of the system: the opposite of its effect in the rest of parameter space. We also find that reducing $\alpha$ below zero increases $T_c$ and that the effect of backreaction is diminished. We study the zero temperature limit, proving that this system does not permit regular solutions for a non-trivial, tachyonic scalar field and constrain possible solutions for fields with positive masses. We investigate singular, zero temperature solutions in the Einstein limit but find them to be incompatible with the concept of GB gravity being a perturbative expansion of Einstein gravity. We study the conductivity of the system, finding that the inclusion of backreaction hinders the development of poles in the conductivity that are associated with quasi-normal modes approaching the real axis from elsewhere in the complex plane.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study fully backreacting, Gauss-Bonnet (GB) holographic superconductors in 5 bulk spacetime dimensions. | contribution 1.00 | 0.94 | 0.04 | asserted 0.91 |
| s1 | We explore the system's dependence on the scalar mass for both positive and negative GB coupling, $\alpha$. | contribution 0.97 | 0.91 | 0.03 | asserted 0.81 |
| s2 | We find that when the mass approaches the Breitenlohner-Freedman (BF) bound and $\alpha\rightarrow L^2/4$ the effect of backreaction is to increase the critical temperature, $T_c$, of the system: the opposite of its effect in the rest of parameter space. | result 1.00 | 0.97 | 0.44 | asserted 1.00 |
| s3 | We also find that reducing $\alpha$ below zero increases $T_c$ and that the effect of backreaction is diminished. | result 1.00 | 0.97 | 0.14 | asserted 1.00 |
| s4 | We study the zero temperature limit, proving that this system does not permit regular solutions for a non-trivial, tachyonic scalar field and constrain possible solutions for fields with positive masses. | result 0.77 | 0.96 | 0.10 | asserted 1.00 |
| s5 | We investigate singular, zero temperature solutions in the Einstein limit but find them to be incompatible with the concept of GB gravity being a perturbative expansion of Einstein gravity. | result 0.92 | 0.95 | 0.05 | asserted 1.00 |
| s6 | We study the conductivity of the system, finding that the inclusion of backreaction hinders the development of poles in the conductivity that are associated with quasi-normal modes approaching the real axis from elsewhere in the complex plane. | result 1.00 | 0.96 | 0.12 | asserted 1.00 |
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The paper
Original abstract
We study fully backreacting, Gauss-Bonnet (GB) holographic superconductors in 5 bulk spacetime dimensions. We explore the system's dependence on the scalar mass for both positive and negative GB coupling, $\alpha$. We find that when the mass approaches the Breitenlohner-Freedman (BF) bound and $\alpha\rightarrow L^2/4$ the effect of backreaction is to increase the critical temperature, $T_c$, of the system: the opposite of its effect in the rest of parameter space. We also find that reducing $\alpha$ below zero increases $T_c$ and that the effect of backreaction is diminished. We study the zero temperature limit, proving that this system does not permit regular solutions for a non-trivial, tachyonic scalar field and constrain possible solutions for fields with positive masses. We investigate singular, zero temperature solutions in the Einstein limit but find them to be incompatible with the concept of GB gravity being a perturbative expansion of Einstein gravity. We study the conductivity of the system, finding that the inclusion of backreaction hinders the development of poles in the conductivity that are associated with quasi-normal modes approaching the real axis from elsewhere in the complex plane.
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How the literature uses it
8 arXiv papers cite this in 10 sentences
Papers citing it · 7 sentences without a confident label
Cites it as background 3 papers
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The s-wave phase dual to Solution $S_1$ from Einstein-Gauss Bonnet gravity has already been studied in Refs. [ref] .
Competing s-wave orders from Einstein-Gauss-Bonnet gravity · The free energy curve of Solution $S_1$ · 0.96
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These include superconductors in different dimensions [ref] , as well as holographic superconductors in different backgrounds, e.g. in an external magnetic field [ref] , with Weyl corrections [ref] , in Horava-Lifshitz gravity [ref] , Gauss-Bonnet gravity [ref] , and $f(R)$ gravity [ref] .
Higher-dimensional Holographic Superconductors in Born-Infeld Electrodynamics and f(R) Gravity · Introduction · 0.98
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Several other systems in higher dimensions involving the addition of higher curvature terms like the Gauss Bonnet term [ref] and also superconductors arising from nonlinear Born-Infeld electrodynamics [ref] have been studied.
Rotating BTZ Black Holes and One Dimensional Holographic Superconductors · Introduction · 0.93
What it cites · 34 sentences without a confident label
Builds on 1 paper
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This paper expands upon [ref] , studying the fully backreacting holographic superconductor in GB gravity for a variety of scalar masses for positive and negative GB coupling constant $α$.
Gauss-Bonnet Holographic Superconductors · Introduction · 1.00
Uses the method or tool of 6 papers
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In the next section we solve ([ref]-[ref]) numerically, reading this $1/r^Δ_+$ fall off of the scalar field to obtain $⟨O_Δ_+ ⟩$ for a range of temperatures given by [equation] For numerical convenience we will use the scaling symmetries of the metric, [ref] , to set $L=Q=q=1$.
Gauss-Bonnet Holographic Superconductors · The bulk · 0.86
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Instead, to calculate the conductivity we shall follow [ref] and expand the solutions to ([ref]) in the vicinity of the adS boundary, $(r→∞)$ giving [equation] with $a_0$ and $a_2$ being integration constants that are used to calculate the conductivity: [equation] As was noted in [ref] and [ref] there exists an arbitrariness of scale in the logarithmic term in ([ref]) introduced during the holographic renormalization process [ref] .
Lecture Notes on Holographic Renormalization · Conductivity · 0.95
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Instead, to calculate the conductivity we shall follow [ref] and expand the solutions to ([ref]) in the vicinity of the adS boundary, $(r→∞)$ giving [equation] with $a_0$ and $a_2$ being integration constants that are used to calculate the conductivity: [equation] As was noted in [ref] and [ref] there exists an arbitrariness of scale in the logarithmic term in ([ref]) introduced during the holographic renormalization process [ref] .
Holographic Superconductors with Various Condensates · Conductivity · 0.95
Compares with 1 paper
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In [ref] , which studied the $m^2>0$ case in the probe limit, the authors found solutions at larger masses but found that solutions become difficult to attain, possibly due to an observed warping of the solution space which was dramatically enhanced by increasing $m^2$.
Density driven symmetry breaking and Butterfly effect in holographic superconductors · Conclusion · 0.89
Cites as support 1 paper
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In fact, it seems likely that such solutions do exist in light of [ref] , where similar solutions were found for a system in four dimensional Einstein gravity.
Zero Temperature Limit of Holographic Superconductors · Zero Temperature Superconductors · 0.96
Cites as background 18 papers
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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] .
Ground states of holographic superconductors · Introduction · 0.99
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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] .
Stability of Holographic Superconductors · Introduction · 0.99
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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] .
Building an AdS/CFT superconductor · Introduction · 0.99
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