143 research outputs found
Constraints on the second order transport coefficients of an uncharged fluid
In this note we have tried to determine how the existence of a local entropy
current with non-negative divergence constrains the second order transport
coefficients of an uncharged fluid, following the procedure described in
\cite{Romatschke:2009kr}. Just on symmetry ground the stress tensor of an
uncharged fluid can have 15 transport coefficients at second order in
derivative expansion. The condition of entropy-increase gives five relations
among these 15 coefficients. So finally the relativistic stress tensor of an
uncharged fluid can have 10 independent transport coefficients at second order.Comment: 43 page
Relativistic Viscous Fluid Dynamics and Non-Equilibrium Entropy
Fluid dynamics corresponds to the dynamics of a substance in the long
wavelength limit. Writing down all terms in a gradient (long wavelength)
expansion up to second order for a relativistic system at vanishing charge
density, one obtains the most general (causal) equations of motion for a fluid
in the presence of shear and bulk viscosity, as well as the structure of the
non-equilibrium entropy current. Requiring positivity of the divergence of the
non-equilibrium entropy current relates some of its coefficients to those
entering the equations of motion. I comment on possible applications of these
results for conformal and non-conformal fluids.Comment: 25 pages, no figures; v2: matches published versio
Radiation from the non-extremal fuzzball
The fuzzball proposal says that the information of the black hole state is
distributed throughout the interior of the horizon in a `quantum fuzz'. There
are special microstates where in the dual CFT we have `many excitations in the
same state'; these are described by regular classical geometries without
horizons. Jejjala et.al constructed non-extremal regular geometries of this
type. Cardoso et. al then found that these geometries had a classical
instability. In this paper we show that the energy radiated through the
unstable modes is exactly the Hawking radiation for these microstates. We do
this by (i) starting with the semiclassical Hawking radiation rate (ii) using
it to find the emission vertex in the CFT (iii) replacing the Boltzman
distributions of the generic CFT state with the ones describing the microstate
of interest (iv) observing that the emission now reproduces the classical
instability. Because the CFT has `many excitations in the same state' we get
the physics of a Bose-Einstein condensate rather than a thermal gas, and the
usually slow Hawking emission increases, by Bose enhancement, to a classically
radiated field. This system therefore provides a complete gravity description
of information-carrying radiation from a special microstate of the nonextremal
hole.Comment: corrected typo
The Holographic Universe
We present a holographic description of four-dimensional single-scalar
inflationary universes in terms of a three-dimensional quantum field theory.
The holographic description correctly reproduces standard inflationary
predictions in their regime of applicability. In the opposite case, wherein
gravity is strongly coupled at early times, we propose a holographic
description in terms of perturbative QFT and present models capable of
satisfying the current observational constraints while exhibiting a
phenomenology distinct from standard inflation. This provides a qualitatively
new method for generating a nearly scale-invariant spectrum of primordial
cosmological perturbations.Comment: 20 pages, 5 figs; extended version of arXiv:0907.5542 including
background material and detailed derivations. To appear in Proceedings of 1st
Mediterranean Conference on Classical and Quantum Gravit
Holographic Non-Gaussianity
We investigate the non-Gaussianity of primordial cosmological perturbations
within our recently proposed holographic description of inflationary universes.
We derive a holographic formula that determines the bispectrum of cosmological
curvature perturbations in terms of correlation functions of a holographically
dual three-dimensional non-gravitational quantum field theory (QFT). This
allows us to compute the primordial bispectrum for a universe which started in
a non-geometric holographic phase, using perturbative QFT calculations.
Strikingly, for a class of models specified by a three-dimensional
super-renormalisable QFT, the primordial bispectrum is of exactly the
factorisable equilateral form with f_nl^eq=5/36, irrespective of the details of
the dual QFT. A by-product of this investigation is a holographic formula for
the three-point function of the trace of the stress-energy tensor along general
holographic RG flows, which should have applications outside the remit of this
work.Comment: 42 pages, 2 figs, published versio
Hydrodynamics of R-charged D1-branes
We study the hydrodynamic properties of strongly coupled Yang-Mills
theory of the D1-brane at finite temperature and at a non-zero density of
R-charge in the framework of gauge/gravity duality. The gravity dual
description involves a charged black hole solution of an
Einstein-Maxwell-dilaton system in 3 dimensions which is obtained by a
consistent truncation of the spinning D1-brane in 10 dimensions. We evaluate
thermal and electrical conductivity as well as the bulk viscosity as a function
of the chemical potential conjugate to the R-charges of the D1-brane. We show
that the ratio of bulk viscosity to entropy density is independent of the
chemical potential and is equal to . The thermal conductivity and bulk
viscosity obey a relationship similar to the Wiedemann-Franz law. We show that
at the boundary of thermodynamic stability, the charge diffusion mode becomes
unstable and the transport coefficients exhibit critical behaviour. Our method
for evaluating the transport coefficients relies on expressing the second order
differential equations in terms of a first order equation which dictates the
radial evolution of the transport coefficient. The radial evolution equations
can be solved exactly for the transport coefficients of our interest. We
observe that transport coefficients of the D1-brane theory are related to that
of the M2-brane by an overall proportionality constant which sets the
dimensions.Comment: 57 pages, 12 figure
Holography for chiral scale-invariant models
Deformation of any d-dimensional conformal field theory by a constant null
source for a vector operator of dimension (d + z -1) is exactly marginal with
respect to anisotropic scale invariance, of dynamical exponent z. The
holographic duals to such deformations are AdS plane waves, with z=2 being the
Schrodinger geometry. In this paper we explore holography for such chiral
scale-invariant models. The special case of z=0 can be realized with gravity
coupled to a scalar, and is of particular interest since it is related to a
Lifshitz theory with dynamical exponent two upon dimensional reduction. We show
however that the corresponding reduction of the dual field theory is along a
null circle, and thus the Lifshitz theory arises upon discrete light cone
quantization of an anisotropic scale invariant field theory.Comment: 62 pages; v2, published version, minor improvements and references
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Holographic Renormalization for z=2 Lifshitz Space-Times from AdS
Lifshitz space-times with critical exponent z=2 can be obtained by
dimensional reduction of Schroedinger space-times with critical exponent z=0.
The latter space-times are asymptotically AdS solutions of AdS gravity coupled
to an axion-dilaton system and can be uplifted to solutions of type IIB
supergravity. This basic observation is used to perform holographic
renormalization for 4-dimensional asymptotically z=2 locally Lifshitz
space-times by Scherk-Schwarz dimensional reduction of the corresponding
problem of holographic renormalization for 5-dimensional asymptotically locally
AdS space-times coupled to an axion-dilaton system. We can thus define and
characterize a 4-dimensional asymptotically locally z=2 Lifshitz space-time in
terms of 5-dimensional AdS boundary data. In this setup the 4-dimensional
structure of the Fefferman-Graham expansion and the structure of the
counterterm action, including the scale anomaly, will be discussed. We find
that for asymptotically locally z=2 Lifshitz space-times obtained in this way
there are two anomalies each with their own associated nonzero central charge.
Both anomalies follow from the Scherk--Schwarz dimensional reduction of the
5-dimensional conformal anomaly of AdS gravity coupled to an axion-dilaton
system. Together they make up an action that is of the Horava-Lifshitz type
with nonzero potential term for z=2 conformal gravity.Comment: 32 pages, v2: modified discussion of the central charge
Generalized Holographic Quantum Criticality at Finite Density
We show that the near-extremal solutions of Einstein-Maxwell-Dilaton
theories, studied in ArXiv:1005.4690, provide IR quantum critical geometries,
by embedding classes of them in higher-dimensional AdS and Lifshitz solutions.
This explains the scaling of their thermodynamic functions and their IR
transport coefficients, the nature of their spectra, the Gubser bound, and
regulates their singularities. We propose that these are the most general
quantum critical IR asymptotics at finite density of EMD theories.Comment: v4: Corrected the scaling equation for the conductivity in section
9.
Spectral Flow in AdS(3)/CFT(2)
We study the spectral flowed sectors of the H3 WZW model in the context of
the holographic duality between type IIB string theory in AdS(3)x S^3 x T^4
with NSNS flux and the symmetric product orbifold of T^4. We construct
explicitly the physical vertex operators in the flowed sectors that belong to
short representations of the superalgebra, thus completing the bulk-to-boundary
dictionary for 1/2 BPS states. We perform a partial calculation of the string
three-point functions of these operators. A complete calculation would require
the three-point couplings of non-extremal flowed operators in the H3 WZW model,
which are at present unavailable. In the unflowed sector, perfect agreement has
recently been found between the bulk and boundary three-point functions of 1/2
BPS operators. Assuming that this agreement persists in the flowed sectors, we
determine certain unknown three-point couplings in the H3 WZW model in terms of
three-point couplings of affine descendants in the SU(2) WZW model.Comment: 50 pages, 2 figure
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