Large D holography with metric deformations

Abstract

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.

Large D membrane for higher derivative gravity and black hole second law

“…Hence, it is easy to 11 In practice, it is convenient to work in terms of a set of effective gravity equations in a reduced p + 3 dimensional spacetime involving the p + 3 dimensional metric and a dilaton field φ.The results obtained this way can then be recast in terms of quantities in the full D dimensional spacetime. The results obtained are then shown to be independent of the choice of p.The details of this procedure can be found in [13,14,20,21] see that at first subleading order in 1/D the EGB equations when evaluated in the patch coordinates on the ansatz metric, evaluate to a non-zero quantity of the form 12 Since, the part which remains unsolved at the subleading order is only a non-trivial function of the patch radial coordinate R 13 , the necessary corrections need only be functions of the R coordinates. i.e.…”

“…The effective equations in mass momentum formalism in AdS space with boundary metric deformation has been worked out in[12].…”

Holographic Bjorken flow at large-D

“…This translates to parametrically small velocity fields in the hydrodynamic limit. In these situations, the large-D expansion has been shown to be identical to second order hydrodynamics [8,10,11,29], with higher viscous terms relegated to subleading D-corrections. In this paper we will apply this new expansion technique to a purely relativistic set-up, the dynamics of a strongly coupled field theory in n = D − 1 space-time dimensions which experiences a boost invariant expansion, whose hydrodynamic limit is known as Bjorken flow [31].…”

The large D membrane paradigm for general four-derivative theory of gravity with a cosmological constant

“…It will be interesting to extend the analysis to find the dual membranes in more general backgrounds to get a better understanding of the structure of the membrane equations and stress tensor. A first step in this direction in the mass and momentum approach has been taken in [37]. The authors of this paper derived the effective equations in AdS in presence of arbitrary boundary deformation with particular large D scaling.…”

“…We again consider the most general form of δu a 37) and substitute it in the vector membrane equation to get 38) and the frequency of the vector fluctuations to be…”