359 research outputs found
From Petrov-Einstein to Navier-Stokes in Spatially Curved Spacetime
We generalize the framework in arXiv:1104.5502 to the case that an embedding
may have a nonvanishing intrinsic curvature. Directly employing the Brown-York
stress tensor as the fundamental variables, we study the effect of finite
perturbations of the extrinsic curvature while keeping the intrinsic metric
fixed. We show that imposing a Petrov type I condition on the hypersurface
geometry may reduce to the incompressible Navier-Stokes equation for a fluid
moving in spatially curved spacetime in the near-horizon limit.Comment: 17 pages, references added, generalizing the metric form in part 3,
version published in JHE
AdS/CFT duality for non-relativistic field theory
We formulate a correspondence between non-relativistic conformal field
theories (NRCFTs) in d-1 spatial dimensions and gravitational theories in
AdS_{d+2} backgrounds with one compactified lightlike direction. The breaking
of the maximal SO(2,d+1) symmetry of AdS_{d+2} to the non-relativistic
conformal group arises from boundary conditions on bulk fields, without the
need to introduce non-vacuum sources of energy-momentum. As a check of the
proposal, we use the gravitational theory to reproduce the NRCFT state-operator
correspondence between scaling dimensions of primary operators and energy
eigenstates of the non-relativistic system placed in an external harmonic
potential.Comment: 19 pages LaTeX, no figure
The Viscosity Bound Conjecture and Hydrodynamics of M2-Brane Theory at Finite Chemical Potential
Kovtun, Son and Starinets have conjectured that the viscosity to entropy
density ratio is always bounded from below by a universal multiple of
i.e., for all forms of matter. Mysteriously, the
proposed viscosity bound appears to be saturated in all computations done
whenever a supergravity dual is available. We consider the near horizon limit
of a stack of M2-branes in the grand canonical ensemble at finite R-charge
densities, corresponding to non-zero angular momentum in the bulk. The
corresponding four-dimensional R-charged black hole in Anti-de Sitter space
provides a holographic dual in which various transport coefficients can be
calculated. We find that the shear viscosity increases as soon as a background
R-charge density is turned on. We numerically compute the few first corrections
to the shear viscosity to entropy density ratio and surprisingly
discover that up to fourth order all corrections originating from a non-zero
chemical potential vanish, leaving the bound saturated. This is a sharp signal
in favor of the saturation of the viscosity bound for event horizons even in
the presence of some finite background field strength. We discuss implications
of this observation for the conjectured bound.Comment: LaTeX, 26+1 Pages, 4 Figures, Version 2: references adde
Polymer state approximations of Schroedinger wave functions
It is shown how states of a quantum mechanical particle in the Schroedinger
representation can be approximated by states in the so-called polymer
representation. The result may shed some light on the semiclassical limit of
loop quantum gravity.Comment: 11 pages, 1 figure, Conclusions section adde
Wilsonian Approach to Fluid/Gravity Duality
The problem of gravitational fluctuations confined inside a finite cutoff at
radius 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
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 is derived. The
dependence on is interpreted as renormalization group (RG) flow in the
fluid. Taking the cutoff to infinity in an asymptotically AdS context, the
formula for 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 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 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.Comment: 34 pages, harvmac, clarified boundary conditio
Ehlers symmetry at the next derivative order
We analyse four-dimensional gravity in the presence of general curvature
squared corrections and show that Ehlers' SL(2,R) symmetry, which appears in
the reduction of standard gravity to three dimensions, is preserved by the
correction terms. The mechanism allowing this is a correction of the SL(2,R)
transformation laws which resolves problems with the different scaling
behaviour of various terms occurring in the reduction.Comment: 13 pages. v2: updated referenc
Deconstructing holographic liquids
We argue that there exist simple effective field theories describing the
long-distance dynamics of holographic liquids. The degrees of freedom
responsible for the transport of charge and energy-momentum are Goldstone
modes. These modes are coupled to a strongly coupled infrared sector through
emergent gauge and gravitational fields. The IR degrees of freedom are
described holographically by the near-horizon part of the metric, while the
Goldstone bosons are described by a field-theoretical Lagrangian. In the cases
where the holographic dual involves a black hole, this picture allows for a
direct connection between the holographic prescription where currents live on
the boundary, and the membrane paradigm where currents live on the horizon. The
zero-temperature sound mode in the D3-D7 system is also re-analyzed and
re-interpreted within this formalism.Comment: 21 pages, 2 figure
Einstein-Maxwell gravitational instantons and five dimensional solitonic strings
We study various aspects of four dimensional Einstein-Maxwell multicentred
gravitational instantons. These are half-BPS Riemannian backgrounds of minimal
N=2 supergravity, asymptotic to R^4, R^3 x S^1 or AdS_2 x S^2. Unlike for the
Gibbons-Hawking solutions, the topology is not restricted by boundary
conditions. We discuss the classical metric on the instanton moduli space. One
class of these solutions may be lifted to causal and regular multi `solitonic
strings', without horizons, of 4+1 dimensional N=2 supergravity, carrying null
momentum.Comment: 1+30 page
String Theory and Quantum Chromodynamics
I review recent progress on the connection between string theory and quantum
chromodynamics in the context of the gauge/gravity duality. Emphasis is placed
on conciseness and conceptual aspects rather than on technical details. Topics
covered include the large-Nc limit of gauge theories, the gravitational
description of gauge theory thermodynamics and hydrodynamics, and
confinement/deconfinement thermal phase transitions.Comment: 38 pages, 24 figures. Lectures given at the RTN Winter School on
"Strings, Supergravity and Gauge Theories" at CERN on January 15-19, 200
Causality and the AdS Dirichlet problem
The (planar) AdS Dirichlet problem has previously been shown to exhibit
superluminal hydrodynamic sound modes. This problem is defined by bulk
gravitational dynamics with Dirichlet boundary conditions imposed on a rigid
timelike cut-off surface. We undertake a careful examination of this set-up and
argue that, in most cases, the propagation of information between points on the
Dirichlet hypersurface is nevertheless causal with respect to the induced light
cones. In particular, the high-frequency dynamics is causal in this sense.
There are however two exceptions and both involve boundary gravitons whose
propagation is not constrained by the Einstein equations. These occur in i)
AdS, where the boundary gravitons generally do not respect the induced
light cones on the boundary, and ii) Rindler space, where they are related to
the infinite speed of sound in incompressible fluids. We discuss implications
for the fluid/gravity correspondence with rigid Dirichlet boundaries and for
the black hole membrane paradigm.Comment: 29 pages, 5 figures. v2: added refs. v3: minor clarification
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