69 research outputs found
Holography and gravity with a dynamical aether
We study two-dimensional Einstein-aether (or equivalently
Ho\v{r}ava-Lifshitz) gravity, which has an solution. We examine various
properties of this solution in the context of holography. We first show that
the asymptotic symmetry group is the full set of time reparametrizations, the
one-dimensional conformal group. At the same time there are configurations with
finite energy and temperature, which indicate a violation of the Ward identity
associated with one-dimensional conformal invariance. These solutions are
characterized by a universal causal horizon and we show that the associated
entropy of the universal horizon scales with the logarithm of the temperature.
We discuss the puzzles associated with this result and argue that the violation
of the Ward identity is associated with a type of explicit breaking of time
reparametrizations in the hypothetical dimensional dual system.Comment: 19 pages, v2: minor revisions, references adde
The Anomalous Scaling Exponents of Turbulence in General Dimension from Random Geometry
We propose an exact analytical formula for the anomalous scaling exponents of
inertial range structure functions in incompressible fluid turbulence. The
formula is a gravitational Knizhnik-Polyakov-Zamolodchikov (KPZ)-type relation,
and is valid in any number of space dimensions. It incorporates intermittency
by gravitationally dressing the Kolmogorov linear scaling via a coupling to a
random geometry. The formula has one real parameter that depends on
the number of space dimensions. The scaling exponents satisfy the convexity
inequality, and the supersonic bound constraint. They agree with the
experimental and numerical data in two and three space dimensions, and with
numerical data in four space dimensions. Intermittency increases with ,
and in the infinite limit the scaling exponents approach the value
one, as in Burgers turbulence. At large the th order exponent scales as
. We discuss the relation between fluid flows and black hole geometry
that inspired our proposal.Comment: 18 pages, 3 figures; v3: additional clarifications, added references;
v2: improved discussion, added one figur
Holographic Vorticity in the Fluid/Gravity Correspondence
The vorticity statistics characterises both the direct and the inverse
turbulent cascades of two-dimensional fluid flows. The fluid/gravity
correspondence relates fluid flows to black brane dynamics. We construct the
holographic vorticity for relativistic and non-relativistic fluids in terms of
the gravitational black brane data, and relate it to the horizon vorticity
expressed as a Weyl scalar. We discuss the statistical scaling structure of the
horizon geometry.Comment: 13 pages, v2: fixed typos, minor improvement
Horava-Lifshitz Black Hole Hydrodynamics
We consider the holographic hydrodynamics of black holes in generally
covariant gravity theories with a preferred time foliation. Gravitational
perturbations in these theories have spin two and spin zero helicity modes with
generically different speeds. The black hole solutions possess a spacelike
causal boundary called the universal horizon. We relate the flux of the spin
zero perturbation across the universal horizon to the new dissipative transport
in Lifshitz field theory hydrodynamics found in arXiv:1304.7481. We construct
in detail the hydrodynamics of one such black hole solution, and calculate the
ratio of the shear viscosity to the entropy density.Comment: 22 pages; v2: corrected final value of \eta/s, minor clarifications,
fixed typos, added reference
Entanglement and Thermal Entropy of Gauge Fields
We consider the universal logarithmic divergent term in the entanglement
entropy of gauge fields in the Minkowski vacuum with an entangling sphere.
Employing the mapping in arXiv:1102.0440, we analyze the corresponding thermal
entropy on open Einstein universe and on the static patch of de Sitter. Using
the heat kernel of the vector Laplacian we resolve a discrepancy between the
free field calculation and the expected Euler conformal anomaly. The resolution
suggests a modification of the well known formulas for the vacuum expectation
value of the spin-1 energy-momentum tensor on conformally flat space-times.Comment: 17 page
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