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Higher derivative corrections to Lifshitz backgrounds
High Energy Physics - Theory · Submitted 14 May 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim After exhibiting the renormalized Lifshitz scaling solution to the system with parameterized R^2 corrections, we turn to a toy model with coupling g(\phi)C_{\mu\nu\rho\sigma}^2 and demonstrate that such a term can both stabilize the dilaton and resolve the Lifshitz horizon to AdS_2 x R^2.
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The abstract, sentence by sentence
We explore the effect of curvature-square corrections on Lifshitz solutions to the Einstein-Maxwell-dilaton system. After exhibiting the renormalized Lifshitz scaling solution to the system with parameterized R^2 corrections, we turn to a toy model with coupling g(\phi)C_{\mu\nu\rho\sigma}^2 and demonstrate that such a term can both stabilize the dilaton and resolve the Lifshitz horizon to AdS_2 x R^2. As an example, we construct numerical flows from AdS_4 in the UV to an intermediate Lifshitz region and then to AdS_2 x R^2 in the deep IR.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We explore the effect of curvature-square corrections on Lifshitz solutions to the Einstein-Maxwell-dilaton system. | contribution 0.98 | 0.90 | 0.08 | asserted 0.63 |
| s1 | After exhibiting the renormalized Lifshitz scaling solution to the system with parameterized R^2 corrections, we turn to a toy model with coupling g(\phi)C_{\mu\nu\rho\sigma}^2 and demonstrate that such a term can both stabilize the dilaton and resolve the Lifshitz horizon to AdS_2 x R^2. | result 0.69 | 0.91 | 0.66 | asserted 0.99 |
| s2 | As an example, we construct numerical flows from AdS_4 in the UV to an intermediate Lifshitz region and then to AdS_2 x R^2 in the deep IR. | contribution 0.43 | 0.94 | 0.12 | asserted 1.00 |
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The paper
Original abstract
We explore the effect of curvature-square corrections on Lifshitz solutions to the Einstein-Maxwell-dilaton system. After exhibiting the renormalized Lifshitz scaling solution to the system with parameterized R^2 corrections, we turn to a toy model with coupling g(\phi)C_{\mu\nu\rho\sigma}^2 and demonstrate that such a term can both stabilize the dilaton and resolve the Lifshitz horizon to AdS_2 x R^2. As an example, we construct numerical flows from AdS_4 in the UV to an intermediate Lifshitz region and then to AdS_2 x R^2 in the deep IR.
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References
How the literature uses it
16 arXiv papers cite this in 57 sentences
Papers citing it · 36 sentences without a confident label
Builds on it 2 papers
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In this paper we generalize the solutions in [ref] to non-zero $θ$ and study the effects of squared curvature terms on the solutions of hyperscaling violating backgrounds.
Hyperscaling Violating Solution in Coupled Dilaton-Squared Curvature Gravity · Introduction · 1.00
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In this chapter we generalize the solutions in [ref] to non-zero $θ$ and study the effects of squared curvature terms on the solutions of hyperscaling violating backgrounds.
Beyond AdS Space-times, New Holographic Correspondences and Applications · Introduction · 1.00
Uses its method or tool 2 papers
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The conditions that we will impose, similar to [ref] are: 1) $λ, η, γ>0$. 2) There should be a region where $V_eff(ϕ_0)=0$.
Beyond AdS Space-times, New Holographic Correspondences and Applications · Allowed Regions for the Numerical Solution · 0.83
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Shooting method similar to [ref] can be used to build the numerical flow, however for this case, it would be more difficult.
Hyperscaling Violating Solution in Coupled Dilaton-Squared Curvature Gravity · Crossover Estimations · 1.00
Compares with it 4 papers
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For the consistency check, we may notice that if we let $θ=0$ and set the dimension $d^'=d-1$, these solution will exactly match with the Lifshitz solution found in [ref] and for their case of $d=1$ and 2, the factor of Gauss-Bonnet combination does not contribute to the equation of motion as we expect from the theory of Gauss-Bonnet gravity.
Hyperscaling Violating Solution in Coupled Dilaton-Squared Curvature Gravity · General Solution · 1.00
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Letting $θ=0$ in our results, the solution of [ref] can be re-derived.
Beyond AdS Space-times, New Holographic Correspondences and Applications · Introduction · 0.83
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Let us now check that the result obtained for the toy-model [ref] is indeed correct also for the exact numerical solution found in [ref] (here $d=2$).
What do non-relativistic CFTs tell us about Lifshitz spacetimes? · No smearing function $⇔$ singularities? · 0.88
Cites it as background 5 papers
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The holographic system we use is an $AdS_2×R^2$ geometry (with a hard wall cutoff) supported by a magnetic field; this type of geometry is known to be the near-horizon region of extremal Reissner-Nordstrom black branes, as well as an endpoint of IR flows in more general Einstein-Maxwell-Dilaton (EMD) systems [ref] .
Crystalline Scaling Geometries from Vortex Lattices · Introduction · 0.85
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By now, there are several known ways to resolve this issue [ref] .
What do non-relativistic CFTs tell us about Lifshitz spacetimes? · Lifshitz geodesics · 0.80
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The gravity models in which solutions of this kind have been found and studied include for example Einstein-Maxwell-Dilaton (EMD) [ref] , Supergravity and String Theory [ref] and EMD plus curvature-squared terms [ref] .
Higher-curvature corrections to holographic entanglement entropy in geometries with hyperscaling violation · Introduction · 0.93
What it cites · 22 sentences without a confident label
Compares with 1 paper
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Although in general there is a mixing of $ϕ$ with $a$ and $b$ due to the dilaton coupling to $C_μνρσ^2$, one can check that for $g(ϕ)≡0$ the ansatz [ref] reproduces the purely dilatonic perturbations of the two-derivative theory [ref] .
Resolving Lifshitz Horizons · Perturbations around $AdS_2×ℝ^2$ · 0.85
Cites as support 3 papers
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Some compelling evidence supporting this point of view has been presented in [ref] .
Resolving Lifshitz Horizons · Smoothing out the singularity · 0.99
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Some compelling evidence supporting this point of view has been presented in [ref] .
The Benefits of Stress: Resolution of the Lifshitz Singularity · Smoothing out the singularity · 0.99
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Some compelling evidence supporting this point of view has been presented in [ref] .
On the IR completion of geometries with hyperscaling violation · Smoothing out the singularity · 0.99
Cites as background 16 papers
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A simple realization is to take an Einstein-Maxwell-dilaton system of the form [ref] [equation] Lifshitz scaling is obtained by taking a single exponential for the gauge kinetic function along with a constant potential [Backgrounds dual to systems exhibiting hyperscaling violation may be obtained by instead taking an exponential potential. ] [equation] The scaling solution has a running dilaton and a dynamical exponent given by the relation [equation] In addition, full solutions may be constructed that interpolate between AdS$_d+1$ in the UV and Lifshitz in the IR.
Domain Wall Holography for Finite Temperature Scaling Solutions · Introduction · 0.86
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A simple realization is to take an Einstein-Maxwell-dilaton system of the form [ref] [equation] Lifshitz scaling is obtained by taking a single exponential for the gauge kinetic function along with a constant potential [Backgrounds dual to systems exhibiting hyperscaling violation may be obtained by instead taking an exponential potential. ] [equation] The scaling solution has a running dilaton and a dynamical exponent given by the relation [equation] In addition, full solutions may be constructed that interpolate between AdS$_d+1$ in the UV and Lifshitz in the IR.
Phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime · Introduction · 0.86
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A simple realization is to take an Einstein-Maxwell-dilaton system of the form [ref] [equation] Lifshitz scaling is obtained by taking a single exponential for the gauge kinetic function along with a constant potential [Backgrounds dual to systems exhibiting hyperscaling violation may be obtained by instead taking an exponential potential. ] [equation] The scaling solution has a running dilaton and a dynamical exponent given by the relation [equation] In addition, full solutions may be constructed that interpolate between AdS$_d+1$ in the UV and Lifshitz in the IR.
Holography of Dyonic Dilaton Black Branes · Introduction · 0.86
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