40 research outputs found
Perturbations of moving membranes in AdS_7
We study the stability of uniformly moving membrane-like objects in seven
dimensional Anti-de Sitter space. This is approached by a linear perturbation
analysis and a search for growing modes. We examine both analytic and numerical
configurations previously found in [1].Comment: 20 pages, 6 figure
New Insights into Properties of Large-N Holographic Thermal QCD at Finite Gauge Coupling at (the Non-Conformal/Next-to) Leading Order in N
In the context of [1]'s string theoretic dual of large-N thermal QCD-like
theories at finite gauge/string coupling (as part of the `MQGP' limit of [2]),
we discuss the following. First, up to LO in N, using the results of [3], we
show that the local T^3 of [2] is the T^2-invariant sLag of [3] in a resolved
conifold. This, together with the results of [4], shows that for a
(predominantly resolved or deformed) resolved warped deformed conifold, the
local T^3 of [2] in the MQGP limit, is the T^2-invariant sLag of [3] justifying
the construction of the delocalized SYZ type IIA mirror of the type IIB
background of [1]. Then, using the prescription of [5], we obtain the
temperature dependence of the thermal (and electrical) conductivity working up
to leading order in N (the number of D3-branes), and upon comparison with [6]
show that the results mimic a 1+1-dimensional Luttinger liquid with impurities.
Further, including sub-leading non-conformal terms in the metric determined by
M (the number of fractional D-branes = the number of colors = 3 in the IR after
the end of a Seiberg duality cascade), by looking at respectively the scalar,
vector and tensor modes of metric perturbations and using [7]'s prescription of
constructing appropriate gauge-invariant perturbations, we obtain respectively
the speed of sound, the diffusion constant and the shear viscosity \eta (and
\eta/s) including the non-conformal O((g_s M^2) (g_s N_f)/N<<1)-corrections,
N_f being the number of flavor D7-branes.Comment: 1+75 pages, LaTeX; Some corrections in Tc-related calculations,
results unchange
black hole at N=2 supergravity
In this paper, we consider the charged non-extremal black hole at five
dimensional N = 2 supergravity. We study thermodynamics of AdS_{5} black hole
with three equal charges (q_{1} = q_{2} = q_{3} = q). We obtain Schrodinger
like equation and discuss the effective potential. Then, we consider the case
of the perturbed dilaton field background and find presence of odd coefficients
of the wave function. Also we find that the higher derivative corrections have
no effect on the first and second even coefficients of the wave function.Comment: 17 pages, 4 figures. Published versio
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
Conductivity and quasinormal modes in holographic theories
We show that in field theories with a holographic dual the retarded Green's
function of a conserved current can be represented as a convergent sum over the
quasinormal modes. We find that the zero-frequency conductivity is related to
the sum over quasinormal modes and their high-frequency asymptotics via a sum
rule. We derive the asymptotics of the quasinormal mode frequencies and their
residues using the phase-integral (WKB) approach and provide analytic insight
into the existing numerical observations concerning the asymptotic behavior of
the spectral densities.Comment: 24 pages, 3 figure
Bulk spectral function sum rule in QCD-like theories with a holographic dual
We derive the sum rule for the spectral function of the stress-energy tensor
in the bulk (uniform dilatation) channel in a general class of strongly coupled
field theories. This class includes theories holographically dual to a theory
of gravity coupled to a single scalar field, representing the operator of the
scale anomaly. In the limit when the operator becomes marginal, the sum rule
coincides with that in QCD. Using the holographic model, we verify explicitly
the cancellation between large and small frequency contributions to the
spectral integral required to satisfy the sum rule in such QCD-like theories.Comment: 16 pages, 2 figure
Degenerate Rotating Black Holes, Chiral CFTs and Fermi Surfaces I - Analytic Results for Quasinormal Modes
In this work we discuss charged rotating black holes in
that degenerate to extremal black holes with zero entropy. These black holes
have scaling properties between charge and angular momentum similar to those of
Fermi surface operators in a subsector of SYM. We add a
massless uncharged scalar to the five dimensional supergravity theory, such
that it still forms a consistent truncation of the type IIB ten dimensional
supergravity and analyze its quasinormal modes. Separating the equation of
motion to a radial and angular part, we proceed to solve the radial equation
using the asymptotic matching expansion method applied to a Heun equation with
two nearby singularities. We use the continued fraction method for the angular
Heun equation and obtain numerical results for the quasinormal modes. In the
case of the supersymmetric black hole we present some analytic results for the
decay rates of the scalar perturbations. The spectrum of quasinormal modes
obtained is similar to that of a chiral 1+1 CFT, which is consistent with the
conjectured field-theoretic dual. In addition, some of the modes can be found
analytically.Comment: 41 pages, 1 figure, LaTeX; v2: typos corrected, references adde
From Navier-Stokes To Einstein
We show by explicit construction that for every solution of the
incompressible Navier-Stokes equation in dimensions, there is a uniquely
associated "dual" solution of the vacuum Einstein equations in
dimensions. The dual geometry has an intrinsically flat timelike boundary
segment whose extrinsic curvature is given by the stress tensor of
the Navier-Stokes fluid. We consider a "near-horizon" limit in which
becomes highly accelerated. The near-horizon expansion in gravity is shown to
be mathematically equivalent to the hydrodynamic expansion in fluid dynamics,
and the Einstein equation reduces to the incompressible Navier-Stokes equation.
For , we show that the full dual geometry is algebraically special Petrov
type II. The construction is a mathematically precise realization of
suggestions of a holographic duality relating fluids and horizons which began
with the membrane paradigm in the 70's and resurfaced recently in studies of
the AdS/CFT correspondence.Comment: 15 pages, 2 figures, typos correcte