Holographic turbulence in a large number of dimensions

We use gauge/gravity duality to study the dynamics of strongly coupled gauge theories undergoing boost invariant expansion in an arbitrary number of space-time dimensions (D). By keeping the scale of the late-time energy density fixed, we explore the infinite-D limit and study the first few corrections to this expansion. In agreement with other studies, we find that the large-D dynamics are controlled by hydrodynamics and we use our computation to constrain the leading large-D dependence of a certain combination of transport coefficients up to 6 th order in gradients. Going beyond late time physics, we discuss how non-hydrodynamic modes appear in the large-D expansion in the form of a trans-series in D, identical to the non-perturbative contributions to the gradient expansion. We discuss the consequence of this trans-series in the non-convergence of the large-D expansion.

Section: Introductionmentioning

confidence: 99%

Holographic Bjorken flow at large-D

Casalderrey-Solana

Herzog

Meiring

2019

“…where α is an arbitrary φ-normalisation. Following [15,16] we adopt a Bondi-type ansatz for neutral branes, with the coordinate R = r n ,…”

Section: Introductionmentioning

confidence: 99%

Large D holography with metric deformations

Andrade

Pantelidou

Withers

2018

We consider Einstein gravity in AdS in the presence of a deformed conformal boundary metric, in the limit of large spacetime dimension. At leading order we find a new set of effective near-horizon equations. These can be understood as covariant generalisations of the undeformed equations with new source terms due to the curvature. We show that these equations are given by the conservation of the exact second-order Landau-frame hydrodynamic stress tensor. No derivative expansions are invoked in this identification. We use the new equations to study CFTs with 2d lattice deformations, computing their quasi-normal mode spectra and thermal conductivities, both numerically and analytically to quartic order in small lattice amplitude. Many of our results also apply to asymptotically flat spacetimes.

“…In fact it is expected that this equivalence is valid to all orders [16]. In other words, in the overlap regime, these two equations must be exactly equivalent to each other if we consider all orders on both sides [16], though to see this equivalence we need to re-express the variables of one side in terms of the other [16,19,25]. This equivalence actually involves some interesting resum of one series into the other.…”

Section: Resultsmentioning

confidence: 99%

“…Indeed the results in [5] seem to indicate that terms of different derivative orders in hydrodynamic stress tensor, dual to gravity are weighted by factors of r H ∼ T (x) D , and not T alone. Note that here the temperature of the fluid would scale as D, which is different from the D scaling of the temperature, imposed in [19]. 7 Note that the scaling of λ with D is upto us.…”

Section: Perturbation Parameter Inmentioning

confidence: 89%

“…After implementing the correct gauge transformation, we finally get a field redefinition of the fluid variables (i.e., fluid velocity and the temperature) in terms of membrane velocity and its shape 4 . We hope such a rewriting would lead to some new ways to view fluid and membrane dynamics and more ambitiously to a new duality between fluid and membrane dynamics in large number of dimensions, where gravity has no role to play (See [19], [16] for a similar discussion on such field redefinition and rewriting of fluid equations though in [19] the authors have taken the large D limit in a little different way than ours).…”

Section: Introductionmentioning

confidence: 91%

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A leading-order comparison between fluid-gravity and membrane-gravity dualities

Bhattacharyya

Biswas

Patra

2019

In this note, we have compared two different perturbation techniques that are used to generate dynamical black-brane solutions to Einstein's equations in presence of negative cosmological constant. One is the 'derivative expansion', where the gravity solutions are in one-to-one correspondence with the solutions of relativistic Navier-Stokes equation. The second is the expansion in terms of inverse power of space-time dimensions and here the gravity solutions are dual to a co-dimension one dynamical membrane, embedded in AdS space and coupled to a velocity field. We have shown that in large number of space-time dimensions, there exists an overlap regime between these two perturbation techniques and we matched the two gravity solutions along with their dual systems upto the first non-trivial order in the expansion parameter on both sides. In the process, we established a one-to-one map between dynamical black-brane geometry and the AdS space, which exists even when the number of dimensions is finite.