Large D holography with metric deformations

TL;DR

This paper develops effective near-horizon equations for Einstein gravity in AdS with deformed boundary metrics at large dimensions, linking them to hydrodynamics and applying to CFTs with lattice deformations.

Contribution

It introduces a new set of covariant near-horizon equations incorporating boundary curvature effects, connecting them to second-order hydrodynamics without derivative expansions.

Findings

Derived effective equations for deformed AdS boundaries.

Computed quasi-normal modes and conductivities for lattice-deformed CFTs.

Results applicable to asymptotically flat spacetimes.

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.