Person:

Strominger, Andrew

We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in (p + 1) dimensions, there is a uniquely associated “dual” solution of the vacuum Einstein equations in (p + 2) dimensions. The dual geometry has an intrinsically flat timelike boundary segment (\sum_c) whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a “near-horizon” limit in which (\sum_c) becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation. For (p = 2), we show that the full dual geometry is algebraically special Petrov type II. The construction is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70’s and resurfaced recently in studies of the AdS/CFT correspondence.

Extremal but non-supersymmetric charged black holes with (SU(2)_L) spin in IIB string theory compactified to five dimensions on (K^3 \times S^1) are considered. These have a near-horizon or NHEK region with an enhanced (SL(2, R)_L) conformal symmetry. It is shown that the NHEK geometry has a second, inequivalent, asymptotically flat extension in which the radius of the (S^1) becomes infinite but the radius of the angular circles of (SU(2)_L) orbits approach a constant. The asymptotic charges associated to the second solution identify it as a 5D D1-D5-Taub-NUT black string with certain nonzero worldvolume charge densities, temperatures and chemical potentials. The dual of the NHEK geometry is then identified as an IR limit of this wrapped brane configuration.

We consider asymptotically future de Sitter spacetimes endowed with an eternal observatory. In the conventional descriptions, the conformal metric at the future boundary (I^+) is deformed by the flux of gravitational radiation. We however impose an unconventional future “Dirichlet” boundary condition requiring that the conformal metric is flat everywhere except at the conformal point where the observatory arrives at (I^+). This boundary condition violates conventional causality, but we argue the causality violations cannot be detected by any experiment in the observatory. We show that the bulk-to-bulk two-point functions obeying this future boundary condition are not realizable as operator correlation functions in any normalizable de Sitter invariant vacuum, but they do agree with those obtained by double analytic continuation from anti-de Sitter space.

String theory contains solutions with (SL(2, \mathbb{R})_R \times U(1)_L)-invariant warped (AdS_3) ((WAdS_3)) factors arising as continuous deformations of ordinary (AdS_3) factors. We propose that some of these are holographically dual to the IR limits of nonlocal dipole-deformed 2D D-brane gauge theories, referred to as “dipole CFTs”. Neither the bulk nor boundary theories are currently well-understood, and consequences of the proposed duality for both sides is investigated. The bulk entropy-area law suggests that dipole CFTs have (at large N) a high-energy density of states which does not depend on the deformation parameter. Putting the boundary theory on a spatial circle leads to closed timelike curves in the bulk, suggesting a relation of the latter to dipole-type nonlocality.