Vyacheslav Lysov

BMS supertranslations and Weinberg’s soft graviton theorem

A bstractRecently it was conjectured that a certain infinite-dimensional “diagonal” subgroup of BMS supertranslations acting on past and future null infinity ( and ) is an exact symmetry of the quantum gravity S-matrix, and an associated Ward identity was derived. In this paper we show that this supertranslation Ward identity is precisely equivalent to Weinberg’s soft graviton theorem. Along the way we construct the canonical generators of supertranslations at , including the relevant soft graviton contributions. Boundary conditions at the past and future of and a correspondingly modified Dirac bracket are required. The soft gravitons enter as boundary modes and are manifestly the Goldstone bosons of spontaneously broken supertranslation invariance.

Wilsonian approach to fluid/gravity duality

The problem of gravitational fluctuations confined inside a finite cutoff at radius r = rc outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff rc the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant D (rc) is derived. The dependence on rc is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for D(∞) reproduces as a special case well-known results derived using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound goes to infinity, the fluid becomes incompressible and the Navier-Stokes dispersion relation becomes exact. The resulting universal formula for the diffusion constant D(horizon) reproduces old results from the membrane paradigm. Hence the old membrane paradigm results and new AdS/CFT results are related by RG flow. RG flow-invariance of the viscosity to entropy ratio

Semiclassical Virasoro symmetry of the quantum gravity

\frac{\eta }{s}

\mathcal{S}

is shown to follow from the first law of thermodynamics together with isentropy of radial evolution in classical gravity. The ratio is expected to run when quantum gravitational corrections are included.

-matrix

A bstractIt is shown that the tree-level S

Cargese Lectures on the Kerr/CFT Correspondence

\mathcal{S}

Quasinormal quantization in de Sitter spacetime

-matrix for quantum gravity in four-dimensional Minkowski space has a Virasoro symmetry which acts on the conformal sphere at null infinity.

Lectures on the Kerr/CFT Correspondence

A bstractWe 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 Σc whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a “near-horizon” limit in which Σc 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.