119 research outputs found
The ultraviolet limit and sum rule for the shear correlator in hot Yang-Mills theory
We determine a next-to-leading order result for the correlator of the shear
stress operator in high-temperature Yang-Mills theory. The computation is
performed via an ultraviolet expansion, valid in the limit of small distances
or large momenta, and the result is used for writing operator product
expansions for the Euclidean momentum and coordinate space correlators as well
as for the Minkowskian spectral density. In addition, our results enable us to
confirm and refine a shear sum rule originally derived by Romatschke, Son and
Meyer.Comment: 16 pages, 2 figures. v2: small clarifications, one reference added,
published versio
Shear Modes, Criticality and Extremal Black Holes
We consider a (2+1)-dimensional field theory, assumed to be holographically
dual to the extremal Reissner-Nordstrom AdS(4) black hole background, and
calculate the retarded correlators of charge (vector) current and
energy-momentum (tensor) operators at finite momentum and frequency. We show
that, similar to what was observed previously for the correlators of scalar and
spinor operators, these correlators exhibit emergent scaling behavior at low
frequency. We numerically compute the electromagnetic and gravitational
quasinormal frequencies (in the shear channel) of the extremal
Reissner-Nordstrom AdS(4) black hole corresponding to the spectrum of poles in
the retarded correlators. The picture that emerges is quite simple: there is a
branch cut along the negative imaginary frequency axis, and a series of
isolated poles corresponding to damped excitations. All of these poles are
always in the lower half complex frequency plane, indicating stability. We show
that this analytic structure can be understood as the proper limit of finite
temperature results as T is taken to zero holding the chemical potential fixed.Comment: 28 pages, 7 figures, added reference
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
Higher spin fermions in the BTZ black hole
Recently it has been shown that the wave equations of bosonic higher spin
fields in the BTZ background can be solved exactly. In this work we extend this
analysis to fermionic higher spin fields. We solve the wave equations for
arbitrary half-integer spin fields in the BTZ black hole background and obtain
exact expressions for their quasinormal modes. These quasinormal modes are
shown to agree precisely with the poles of the corresponding two point function
in the dual conformal field theory as predicted by the AdS/CFT correspondence.
We also obtain an expression for the 1-loop determinant in terms of the
quasinormal modes and show it agrees with that obtained by integrating the heat
kernel found by group theoretic methods.Comment: 29 page
Mixed RG Flows and Hydrodynamics at Finite Holographic Screen
We consider quark-gluon plasma with chemical potential and study
renormalization group flows of transport coefficients in the framework of
gauge/gravity duality. We first study them using the flow equations and compare
the results with hydrodynamic results by calculating the Green functions on the
arbitrary slice. Two results match exactly. Transport coefficients at arbitrary
scale is ontained by calculating hydrodynamics Green functions. When either
momentum or charge vanishes, transport coefficients decouple from each other.Comment: 22 pages, 6 figure
Shear sum rules at finite chemical potential
We derive sum rules which constrain the spectral density corresponding to the
retarded propagator of the T_{xy} component of the stress tensor for three
gravitational duals. The shear sum rule is obtained for the gravitational dual
of the N=4 Yang-Mills, theory of the M2-branes and M5-branes all at finite
chemical potential. We show that at finite chemical potential there are
additional terms in the sum rule which involve the chemical potential. These
modifications are shown to be due to the presence of scalars in the operator
product expansion of the stress tensor which have non-trivial vacuum
expectation values at finite chemical potential.Comment: The proof for the absence of branch cuts is corrected.Results
unchange
Hydrodynamics of fundamental matter
First and second order transport coefficients are calculated for the strongly
coupled N=4 SYM plasma coupled to massless fundamental matter in the Veneziano
limit. The results, including among others the value of the bulk viscosity and
some relaxation times, are presented at next-to-leading order in the flavor
contribution. The bulk viscosity is found to saturate Buchel's bound. This
result is also captured by an effective single-scalar five-dimensional
holographic dual in the Chamblin-Reall class and it is suggested to hold, in
the limit of small deformations, for generic plasmas with gravity duals,
whenever the leading conformality breaking effects are driven by marginally
(ir)relevant operators. This proposal is then extended to other relations for
hydrodynamic coefficients, which are conjectured to be universal for every
non-conformal plasma with a dual Chamblin-Reall-like description. Our analysis
extends to any strongly coupled gauge theory describing the low energy dynamics
of Nc>>1 D3-branes at the tip of a generic Calabi-Yau cone. The fundamental
fields are added by means of 1<<Nf<<Nc homogeneously smeared D7-branes.Comment: 24 pages. V2: Important improvements in the discussion of the results
in section 1. References adde
Holographic GB gravity in arbitrary dimensions
We study the properties of the holographic CFT dual to Gauss-Bonnet gravity
in general dimensions. We establish the AdS/CFT dictionary and in
particular relate the couplings of the gravitational theory to the universal
couplings arising in correlators of the stress tensor of the dual CFT. This
allows us to examine constraints on the gravitational couplings by demanding
consistency of the CFT. In particular, one can demand positive energy fluxes in
scattering processes or the causal propagation of fluctuations. We also examine
the holographic hydrodynamics, commenting on the shear viscosity as well as the
relaxation time. The latter allows us to consider causality constraints arising
from the second-order truncated theory of hydrodynamics.Comment: 48 pages, 9 figures. v2: New discussion on free fields in subsection
3.3 and new appendix B on conformal tensor fields. Added comments on the
relation between the central charge appearing in the two-point function and
the "central charge" characterizing the entropy density in the discussion.
References adde
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
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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