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Breaking rotations without violating the KSS viscosity bound
High Energy Physics - Theory · Submitted 4 Apr 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Thus, our construction shows that the breaking of rotations itself does not necessarily imply a violation of the KSS bound.
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The abstract, sentence by sentence
We revisit the computation of the shear viscosity to entropy ratio in a holographic p-wave superfluid model, focusing on the role of rotational symmetry breaking. We study the interplay between explicit and spontaneous symmetry breaking and derive a simple horizon formula for $\eta/s$, which is valid also in the presence of explicit breaking of rotations and is in perfect agreement with the numerical data. We observe that a source which explicitly breaks rotational invariance suppresses the value of $\eta/s$ in the broken phase, competing against the effects of spontaneous symmetry breaking. However, $\eta/s$ always reaches a constant value in the limit of zero temperature, which is never smaller than the Kovtun-Son-Starinets (KSS) bound, $1/4\pi$. This behavior appears to be in contrast with previous holographic anisotropic models which found a power-law vanishing of $\eta/s$ at small temperature. This difference is shown to arise from the properties of the near-horizon geometry in the extremal limit. Thus, our construction shows that the breaking of rotations itself does not necessarily imply a violation of the KSS bound.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We revisit the computation of the shear viscosity to entropy ratio in a holographic p-wave superfluid model, focusing on the role of rotational symmetry breaking. | contribution 0.74 | 0.81 | 0.04 | unclear 0.57 |
| s1 | We study the interplay between explicit and spontaneous symmetry breaking and derive a simple horizon formula for $\eta/s$, which is valid also in the presence of explicit breaking of rotations and is in perfect agreement with the numerical data. | contribution 0.85 | 0.97 | 0.16 | asserted 1.00 |
| s2 | We observe that a source which explicitly breaks rotational invariance suppresses the value of $\eta/s$ in the broken phase, competing against the effects of spontaneous symmetry breaking. | result 1.00 | 0.93 | 0.08 | asserted 1.00 |
| s3 | However, $\eta/s$ always reaches a constant value in the limit of zero temperature, which is never smaller than the Kovtun-Son-Starinets (KSS) bound, $1/4\pi$. | result 1.00 | 0.92 | 0.36 | asserted 1.00 |
| s4 | This behavior appears to be in contrast with previous holographic anisotropic models which found a power-law vanishing of $\eta/s$ at small temperature. | result 0.58 | 0.19 | 0.05 | hedged possibility 0.61 |
| s5 | This difference is shown to arise from the properties of the near-horizon geometry in the extremal limit. | interpretation 0.92 | 0.86 | 0.05 | asserted 1.00 |
| s6 | Thus, our construction shows that the breaking of rotations itself does not necessarily imply a violation of the KSS bound. | interpretation 0.97 | 0.92 | 0.91 | asserted 0.94 |
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The paper
Original abstract
We revisit the computation of the shear viscosity to entropy ratio in a holographic p-wave superfluid model, focusing on the role of rotational symmetry breaking. We study the interplay between explicit and spontaneous symmetry breaking and derive a simple horizon formula for $\eta/s$, which is valid also in the presence of explicit breaking of rotations and is in perfect agreement with the numerical data. We observe that a source which explicitly breaks rotational invariance suppresses the value of $\eta/s$ in the broken phase, competing against the effects of spontaneous symmetry breaking. However, $\eta/s$ always reaches a constant value in the limit of zero temperature, which is never smaller than the Kovtun-Son-Starinets (KSS) bound, $1/4\pi$. This behavior appears to be in contrast with previous holographic anisotropic models which found a power-law vanishing of $\eta/s$ at small temperature. This difference is shown to arise from the properties of the near-horizon geometry in the extremal limit. Thus, our construction shows that the breaking of rotations itself does not necessarily imply a violation of the KSS bound.
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References
How the literature uses it
7 arXiv papers cite this in 8 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 6 papers
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An alternative approach is based on the gauge/gravity duality, which links a certain gravitational theory to fluid dynamics and offers a novel perspective for calculating transport coefficients [ref] ( see [ref] for recent developments).
A holographic model of magnetohydrodynamics with fortuitous SO(3) symmetry · Introduction · 0.83
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These theories are dual to Einstein gravity coupled to an arbitrary matter sector, with the result ([ref]) relying on the additional assumption that rotational invariance is preserved[For a recent discussion of $η/s$ in anisotropic theories we refer the reader to [ref] .].
Holographic transport beyond the supergravity approximation · Introduction and summary · 0.92
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The study carried out in [ref] focuses on the ratio of $η/s$ in a non-abelian holographic p-wave superfluid model demonstrates that rotational symmetry breaking does not lead to a violation of the KSS bound.
Non-Abelian Exponential Yang-Mills AdS Black Brane and Transport Coefficients · Introduction · 0.81
What it cites · 48 sentences without a confident label
Contests 1 paper
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In other words, this implies that the results of [ref] are not completely capturing the $ω→0$ limit needed to define the shear viscosity coefficient via the corresponding Kubo formula.
Transport in Anisotropic Superfluids: A Holographic Description · Numerical Analysis · contest 0.73
Uses the method or tool of 2 papers
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Following the strategy used in [ref] (see also [ref] ), we expand the metric and gauge field perturbations $Ψ_x$, $a^1_y$, and $a^2_y$ in powers of frequency $ω$,
Odd viscosity in the quantum critical region of a holographic Weyl semimetal · An Analytical Horizon Formula · 1.00
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Following the strategy used in [ref] (see also [ref] ), we expand the metric and gauge field perturbations $Ψ_x$, $a^1_y$, and $a^2_y$ in powers of frequency $ω$,
Holographic Viscoelastic Hydrodynamics · An Analytical Horizon Formula · 1.00
Compares with 7 papers
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In those examples, the IR geometry remains strongly modified near extremality, becoming an AdS$_4$ $×R$ geometry in the case of axion models [ref] or a BTZ black hole times a two-dimensional torus in the case of a magnetic field [ref] , thus explaining the different scaling of the $η/s$ ratio as $T→0$.
A Strongly Coupled Anisotropic Fluid From Dilaton Driven Holography · On the (non) violation of the KSS bound · 0.86
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In those examples, the IR geometry remains strongly modified near extremality, becoming an AdS$_4$ $×R$ geometry in the case of axion models [ref] or a BTZ black hole times a two-dimensional torus in the case of a magnetic field [ref] , thus explaining the different scaling of the $η/s$ ratio as $T→0$.
Momentum transport in strongly coupled anisotropic plasmas in the presence of strong magnetic fields · On the (non) violation of the KSS bound · 0.86
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While our results for the non-universal $η/s$ are in qualitative agreement with those of [ref] , we find a difference in the temperature dependence, which becomes more apparent as the temperature is lowered well below $T_c$.
Transport in Anisotropic Superfluids: A Holographic Description · Numerical Analysis · 0.99
Cites as background 45 papers
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In order to answer these questions, we consider a (five-dimensional) holographic model for p-wave superfluidity, in which a vector condensate breaks simultaneously a U(1) symmetry together with the rotational group SO$(3) →$ SO$(2)$ [ref] (see [ref] for a review of holographic p-wave superfluids).
Introduction to Holographic Superconductor Models · Introduction · 0.81
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In order to answer these questions, we consider a (five-dimensional) holographic model for p-wave superfluidity, in which a vector condensate breaks simultaneously a U(1) symmetry together with the rotational group SO$(3) →$ SO$(2)$ [ref] (see [ref] for a review of holographic p-wave superfluids).
The gravity dual of a p-wave superconductor · Introduction · 0.81
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A third possibility is to break rotations spontaneously in a system undergoing a p-wave superfluid instability [ref] .
Running Shear Viscosities in Anisotropic Holographic Superfluids · Introduction · 0.92
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