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.

25 pages, 6 figures, 2 tables; v2 references added

References in corpus (15)

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• Relativistic viscous hydrodynamics, conformal invariance, and holography
• Momentum dissipation and effective theories of coherent and incoherent transport
• High and Low Dimensions in The Black Hole Negative Mode
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• Phases and Stability of Non-Uniform Black Strings
• Einstein-Gauss-Bonnet Black Strings at Large $D$
• Unstable `black branes' from scaled membranes at large $D$
• On Brane Instabilities in the Large $D$ Limit
• Holographic Turbulence in a Large Number of Dimensions
• Geometric polarization of plasmas and Love numbers of AdS black branes
• The Large Dimension Limit of a Small Black Hole Instability in Anti-de Sitter Space
• Hydrodynamic charge and heat transport on inhomogeneous curved spaces
• Non-linear perturbation of black branes at large $D$
• Cosmic Censorship at Large D: Stability analysis in polarized AdS black branes (holes)

Cited by in corpus (13)

• Holographic Collisions across a Phase Transition
• The Large D Limit of Einstein's Equations
• Rigorous bounds on transport from causality
• Holographic Bjorken Flow at Large-D
• Stationary Solutions from the Large D Membrane Paradigm
• Nambu-Goldstone modes in non-equilibrium systems from AdS/CFT correspondence
• Black Ripples, Flowers and Dumbbells at large $D$
• Holographic Observables at Large $d$
• A leading-order comparison between fluid-gravity and membrane-gravity dualities
• Large D membrane for Higher Derivative Gravity and Black Hole Second Law
• The large $D$ membrane paradigm for general four-derivative theory of gravity with a cosmological constant
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• An analytic approach for holographic entanglement entropy at (quantum) criticality