681 research outputs found
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
Sum rules and three point functions
Sum rules constraining the R-current spectral densities are derived
holographically for the case of D3-branes, M2-branes and M5-branes all at
finite chemical potentials. In each of the cases the sum rule relates a certain
integral of the spectral density over the frequency to terms which depend both
on long distance physics, hydrodynamics and short distance physics of the
theory. The terms which which depend on the short distance physics result from
the presence of certain chiral primaries in the OPE of two R-currents which are
turned on at finite chemical potential. Since these sum rules contain
information of the OPE they provide an alternate method to obtain the structure
constants of the two R-currents and the chiral primary. As a consistency check
we show that the 3 point function derived from the sum rule precisely matches
with that obtained using Witten diagrams.Comment: 41 page
The Sound of Topology in the AdS/CFT Correspondence
Using the gauge/gravity correspondence, we study the properties of 2-point
correlation functions of finite-temperature strongly coupled gauge field
theories, defined on a curved space of general spatial topology with a dual
black hole description. We derive approximate asymptotic expressions for the
correlation functions and their poles, supported by exact numerical
calculations, and study their dependence on the dimension of spacetime and the
spatial topology. The asymptotic structure of the correlation functions depends
on the relation between the spatial curvature and the temperature, and is
noticeable when they are of the same order. In the case of a hyperbolic
topology, a specific temperature is identified for which exact analytical
solutions exist for all types of perturbations. The asymptotic structure of the
correlation functions poles is found to behave in a non-smooth manner when
approaching this temperature.Comment: 65 pages, LaTeX, 21 figures, 1 table; fixed a small error in
subsection 3.
Viscosity Bound and Causality in Superfluid Plasma
It was argued by Brigante et.al that the lower bound on the ratio of the
shear viscosity to the entropy density in strongly coupled plasma is translated
into microcausality violation in the dual gravitational description. Since
transport properties of the system characterize its infrared dynamics, while
the causality of the theory is determined by its ultraviolet behavior, the
viscosity bound/microcausality link should not be applicable to theories that
undergo low temperature phase transitions. We present an explicit model of
AdS/CFT correspondence that confirms this fact.Comment: 27 pages, 5 figures. References added, typos fixe
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
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
Nonlinear Hydrodynamics from Flow of Retarded Green's Function
We study the radial flow of retarded Green's function of energy-momentum
tensor and -current of dual gauge theory in presence of generic higher
derivative terms in bulk Lagrangian. These are first order non-linear Riccati
equations. We solve these flow equations analytically and obtain second order
transport coefficients of boundary plasma. This way of computing transport
coefficients has an advantage over usual Kubo approach. The non-linear equation
turns out to be a linear first order equation when we study the Green's
function perturbatively in momentum. We consider several examples including
term and generic four derivative terms in bulk. We also study the flow
equations for -charged black holes and obtain exact expressions for second
order transport coefficients for dual plasma in presence of arbitrary chemical
potentials. Finally we obtain higher derivative corrections to second order
transport coefficients of boundary theory dual to five dimensional gauge
supergravity.Comment: Version 2, reference added, typos correcte
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
Higher spin quasinormal modes and one-loop determinants in the BTZ black hole
We solve the wave equations of arbitrary integer spin fields in the BTZ black
hole background and obtain exact expressions for their quasinormal modes. We
show that these quasinormal modes precisely agree with the location of the
poles of the corresponding two point function in the dual conformal field
theory as predicted by the AdS/CFT correspondence. We then use these
quasinormal modes to construct the one-loop determinant of the higher spin
field in the thermal BTZ background. This is shown to agree with that obtained
from the corresponding heat kernel constructed recently by group theoretic
methods.Comment: 47 page
The momentum analyticity of two-point correlators from perturbation theory and AdS/CFT
The momentum plane analyticity of two point function of a relativistic
thermal field theory at zero chemical potential is explored. A general
principle regarding the location of the singularities is extracted. In the case
of the N=4 supersymmetric Yang-Mills theory at large , a qualitative
change in the nature of the singularity (branch points versus simple poles)
from the weak coupling regime to the strong coupling regime is observed with
the aid of the AdS/CFT correspondence.Comment: 18 pages, 3 figures, typos fixed, 1 figure update
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