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Hyperscaling-Violation on Probe D-Branes
High Energy Physics - Theory · Submitted 6 Jul 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For the field theories dual to D3/D7- and D3/D5-brane systems we find non-relativistic finite density fixed points exhibiting a violation of hyperscaling.
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For the field theories dual to D3/D7- and D3/D5-brane systems we find non-relativistic finite density fixed points exhibiting a violation of hyperscaling. This violation is measured by the critical exponent $\theta=1$ while the dynamical critical exponent is $z=2$. At zero temperature we compute the thermodynamic potentials, the speed of normal sound, and the speed of zero sound for both these massive D3/D(2n+1)-brane systems near their non-relativistic fixed points. Moreover, we determine the first correction to the free energy for small temperatures yielding the critical exponents $\alpha$ and $\nu$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | For the field theories dual to D3/D7- and D3/D5-brane systems we find non-relativistic finite density fixed points exhibiting a violation of hyperscaling. | result 0.97 | 0.95 | 0.78 | asserted 1.00 |
| s1 | This violation is measured by the critical exponent $\theta=1$ while the dynamical critical exponent is $z=2$. | result 1.00 | 0.87 | 0.30 | asserted 1.00 |
| s2 | At zero temperature we compute the thermodynamic potentials, the speed of normal sound, and the speed of zero sound for both these massive D3/D(2n+1)-brane systems near their non-relativistic fixed points. | contribution 0.88 | 0.96 | 0.08 | asserted 1.00 |
| s3 | Moreover, we determine the first correction to the free energy for small temperatures yielding the critical exponents $\alpha$ and $\nu$. | result 0.76 | 0.96 | 0.09 | asserted 1.00 |
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The paper
Original abstract
For the field theories dual to D3/D7- and D3/D5-brane systems we find non-relativistic finite density fixed points exhibiting a violation of hyperscaling. This violation is measured by the critical exponent $\theta=1$ while the dynamical critical exponent is $z=2$. At zero temperature we compute the thermodynamic potentials, the speed of normal sound, and the speed of zero sound for both these massive D3/D(2n+1)-brane systems near their non-relativistic fixed points. Moreover, we determine the first correction to the free energy for small temperatures yielding the critical exponents $\alpha$ and $\nu$.
Human review
References
How the literature uses it
36 arXiv papers cite this in 62 sentences
Papers citing it · 26 sentences without a confident label
Builds on it 3 papers
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Here we will find the critical exponents for the general #ND=4 intersections, generalizing the results of [ref] .
Collective excitations of massive flavor branes · Introduction · 1.00
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Eq. ([ref]) is a generalization of the expression written in [ref] by including a logarithmic multiplicative term with some new exponent $ζ$.
Quantum phase transitions with dynamical flavors · The unflavored transition · 0.99
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In Appendix [ref], we extend this analysis to include groundstates which feature hyperscaling violation [ref] as well as cases with novel superfluid actions.[An analytic top-down solution featuring hyperscaling violation in the normal state can be found in [ref] .] $$
Non-vanishing normal density in cold holographic superfluids · Introduction and results · 0.94
Uses its method or tool 2 papers
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Let us thus follow the approach of [ref] and study the behavior of the system near the quantum critical point at $μ=m$.
Collective excitations of massive flavor branes · Hyperscaling violation near the critical point · 0.93
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Let us determine, following the reasoning in [ref] , the dynamical critical exponent $z$ by dimensional analysis of the dispersion relation of the sound mode, which is of the form $ω = u_s k$, where $u_s$ is given by ([ref]) near the critical point $μ̅=0$.
Quantum phase transitions with dynamical flavors · The unflavored transition · 0.97
Uses its data or values 1 paper
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The EoS is known analytically [ref] , and the pressure, energy density, and mass density at zero temperature read as functions of the chemical potential p=λ(μ^2-m_q^2)^2, ε=λ(μ^2-m_q^2)(3μ^2+m_q^2), ρ=4λm_qμ(μ^2-m_q^2) , where $λ$ is an unimportant constant factor.
Stiff phases in strongly coupled gauge theories with holographic duals · Equation of State · 0.92
Compares with it 2 papers
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Notice that the relation ([ref]) between $θ$ and $z$ coincides with the ones found in [ref] for the D3-D7 system (taking $n=3$ and $λ=6$) and for the D3-D5 intersection (taking $n=2$ and $λ=4$).
Collective excitations of massive flavor branes · Hyperscaling violation near the critical point · 1.00
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This transition is similar to the one that happens in the D$p$-D$q$ systems in [ref] and corresponds to passing from a black hole to a Minkowski embedding.
Quantum phase transitions with dynamical flavors · Introduction · 0.99
Cites it as background 18 papers
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Recently, the Lifshitz-like geometries are extended to even more sophisticated geometries, the so-called hyperscaling violating geometries [ref] , which on top of anisotropic scaling, have also an overall hyperscaling factor under the scaling parameterized by the hyperscaling violation exponent $θ$.
Holographic superconductor in hyperscaling violation geometry with Maxwell-dilaton coupling · Introduction · 0.89
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[ref] , and exhibit many unusual properties.
Moduli Spaces of Cold Holographic Matter · Review: Cold Holographic Matter · 0.94
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A variant of such setups where the gravity solution is not only characterized by a dynamical exponent $z$ (as in the Lifshitz case) but also by the so-called hyperscaling violation exponent $θ$, has recently gained some attention [ref] ; some earlier studies include [ref] .
Quantum Fluctuations in Holographic Theories with Hyperscaling Violation · Introduction · 0.93
What it cites · 33 sentences without a confident label
Uses the method or tool of 3 papers
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Note that we follow in large parts the methods presented in [ref] .
On Stability and Transport of Cold Holographic Matter · Zero sound of D3/D7, D3/D5, and D3/D3 · 1.00
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Note that we follow in large parts the methods presented in [ref] .
Comments on Fermi Liquid from Holography · Zero sound of D3/D7, D3/D5, and D3/D3 · 1.00
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Unfortunately in order to use the Ryu-Takayanagi prescription [ref] one seems to require the fully backreacted solution, so such a calculation is not currently feasible.
Holographic Derivation of Entanglement Entropy from AdS/CFT · Discussion · 0.89
Compares with 3 papers
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Neither in [ref] nor in the present paper does the static coefficient $ν$ mentioned above appear explicitly.
Hidden Fermi surfaces in compressible states of gauge-gravity duality · Introduction · 0.87
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Neither in [ref] nor in the present paper does the static coefficient $ν$ mentioned above appear explicitly.
Aspects of holography for theories with hyperscaling violation · Introduction · 0.87
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For D3/D(2$n$+1) we finally get the dispersion relations [equation] where the subleading terms are given for $n=3$ by [equation] and for $n=2$ by [equation] Note that our result for $n=3$ agrees with the result previously obtained for this case in [ref] (equation (30) therein).
Holographic zero sound at finite temperature · Zero sound of D3/D7, D3/D5, and D3/D3 · 1.00
Cites as support 2 papers
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As theories with a supergravity dual are intrinsically classical and often reproduce mean field results, one should presumably not be surprised that hyperscaling violation is actually the norm in these systems, as seen for example in [ref] .
Critical phenomena in N=2* plasma · Introduction · 0.96
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As theories with a supergravity dual are intrinsically classical and often reproduce mean field results, one should presumably not be surprised that hyperscaling violation is actually the norm in these systems, as seen for example in [ref] .
Critical phenomena in N=4 SYM plasma · Introduction · 0.96
Cites as background 13 papers
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In this section we briefly review the D3/D(2$n$+1)-brane setups at zero temperature, and the implications of their stationary analytic solutions for the thermodynamics of the dual theory [ref] .
Holographic Thermodynamics at Finite Baryon Density: Some Exact Results · Hyperscaling violation from D3/D7 and D3/D5 · 0.97
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In [ref] a particular behavior of the metric on the gravity side was identified to be yielding non-trivial $θ$ and $z$ on the gauge side.
Hidden Fermi surfaces in compressible states of gauge-gravity duality · Introduction · 0.87
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The $N_f$ hypermultiplets propagating in $n+1$ dimensions (where $n$ is the number of spatial dimensions) are represented by $N_f$ D(2$n$+1)–branes [ref] which are aligned as shown in figure [ref].
Adding flavor to AdS/CFT · D3/D(2$n$+1) brane embeddings · 0.94
Discussion
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