Wilsonian Approach to Fluid/Gravity Duality

The problem of gravitational fluctuations confined inside a finite cutoff at radius $r=r_c$ 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 $r_c$ 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 $D(r_c)$ is derived. The dependence on $r_c$ is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for $D(\infty)$ 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 $D(horizon)$ 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 $\eta /s$ 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

AdS_7/CFT_6, Gauss-Bonnet Gravity, and Viscosity Bound

We study the relation between the causality and the positivity of energy bounds in Gauss-Bonnet gravity in AdS_7 background and find a precise agreement. Requiring the group velocity of metastable states to be bounded by the speed of light places a bound on the value of Gauss-Bonnet coupling. To find the positivity of energy constraints we compute the parameters which determine the angular distribution of the energy flux in terms of three independent coefficients specifying the three-point function of the stress-energy tensor. We then relate the latter to the Weyl anomaly of the six-dimensional CFT and compute the anomaly holographically. The resulting upper bound on the Gauss-Bonnet coupling coincides with that from causality and results in a new bound on viscosity/entropy ratio.Comment: 21 page, harvmac; v2: reference adde

Holographic GB gravity in arbitrary dimensions

We study the properties of the holographic CFT dual to Gauss-Bonnet gravity in general $D \ge 5$ 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

Holographic current correlators at finite coupling and scattering off a supersymmetric plasma

By studying the effect of the order(\alpha'^3) string theory corrections to type IIB supergravity, including those corrections involving the Ramond-Ramond five-form field strength, we obtain the corrected equations of motion of an Abelian perturbation of the AdS_5-Schwarzschild black hole. We then use the gauge theory/string theory duality to examine the coupling-constant dependence of vector current correlators associated to a gauged U(1) sub-group of the global R-symmetry group of strongly-coupled N=4 supersymmetric Yang-Mills theory at finite temperature. The corrections induce a set of higher-derivative operators for the U(1) gauge field, but their effect is highly suppressed. We thus find that the order(\alpha'^3) corrections affect the vector correlators only indirectly, through the corrected metric. We apply our results to investigate scattering off a supersymmetric Yang-Mills plasma at low and high energy. In the latter regime, where Deep Inelastic Scattering is expected to occur, we find an enhancement of the plasma structure functions in comparison with the infinite 't Hooft coupling result.Comment: 38 pages, 6 figures, minor clarifications added, typos corrected, references adde

Nonlinear Hydrodynamics from Flow of Retarded Green's Function

We study the radial flow of retarded Green's function of energy-momentum tensor and $R$-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 $Weyl^4$ term and generic four derivative terms in bulk. We also study the flow equations for $R$-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

Holography of Charged Dilaton Black Holes

We study charged dilaton black branes in $AdS_4$. Our system involves a dilaton $\phi$ coupled to a Maxwell field $F_{\mu\nu}$ with dilaton-dependent gauge coupling, ${1\over g^2} = f^2(\phi)$. First, we find the solutions for extremal and near extremal branes through a combination of analytical and numerical techniques. The near horizon geometries in the simplest cases, where $f(\phi) = e^{\alpha\phi}$, are Lifshitz-like, with a dynamical exponent $z$ determined by $\alpha$. The black hole thermodynamics varies in an interesting way with $\alpha$, but in all cases the entropy is vanishing and the specific heat is positive for the near extremal solutions. We then compute conductivity in these backgrounds. We find that somewhat surprisingly, the AC conductivity vanishes like $\omega^2$ at T=0 independent of $\alpha$. We also explore the charged black brane physics of several other classes of gauge-coupling functions $f(\phi)$. In addition to possible applications in AdS/CMT, the extremal black branes are of interest from the point of view of the attractor mechanism. The near horizon geometries for these branes are universal, independent of the asymptotic values of the moduli, and describe generic classes of endpoints for attractor flows which are different from $AdS_2\times R^2$.Comment: 33 pages, 3 figures, LaTex; v2, references added; v3, more refs added; v4, refs added, minor correction

Large N and Bosonization in Three Dimensions

Bosonization is normally thought of as a purely two-dimensional phenomenon, and generic field theories with fermions in D>2 are not expected be describable by local bosonic actions, except in some special cases. We point out that 3D SU(N) gauge theories on R^{1,1} x S^{1}_{L} with adjoint fermions can be bosonized in the large N limit. The key feature of such theories is that they enjoy large N volume independence for arbitrary circle size L. A consequence of this is a large N equivalence between these 3D gauge theories and certain 2D gauge theories, which matches a set of correlation functions in the 3D theories to corresponding observables in the 2D theories. As an example, we focus on a 3D SU(N) gauge theory with one flavor of adjoint Majorana fermions and derive the large-N equivalent 2D gauge theory. The extra dimension is encoded in the color degrees of freedom of the 2D theory. We then apply the technique of non-Abelian bosonization to the 2D theory to obtain an equivalent local theory written purely in terms of bosonic variables. Hence the bosonized version of the large N three-dimensional theory turns out to live in two dimensions.Comment: 30 pages, 2 tables. v2 minor revisions, references adde

Moduli and electromagnetic black brane holography

We investigate the thermodynamic and hydrodynamic properties of 4-dimensional gauge theories with finite electric charge density in the presence of a constant magnetic field. Their gravity duals are planar magnetically and electrically charged AdS black holes in theories that contain a gauge Chern-Simons term. We present a careful analysis of the near horizon geometry of these black branes at finite and zero temperature for the case of a scalar field non-minimally coupled to the electromagnetic field. With the knowledge of the near horizon data, we obtain analytic expressions for the shear viscosity coefficient and entropy density, and also study the effect of a generic set of four derivative interactions on their ratio. We also comment on the attractor flows of the extremal solutions.Comment: 39 pages, no figures; v2: minor changes, refs. added; v3: typo fixed; v4: a proof for decoupling of the viscosity mode added in appendix, matches the published versio

From Navier-Stokes To Einstein

We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in $p+1$ dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in $p+2$ dimensions. The dual geometry has an intrinsically flat timelike boundary segment $\Sigma_c$ whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which $\Sigma_c$ 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 $p=2$, 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

Plasma photoemission from string theory

Leading 't Hooft coupling corrections to the photoemission rate of the planar limit of a strongly-coupled {\cal {N}}=4 SYM plasma are investigated using the gauge/string duality. We consider the full order \alpha'^3 type IIB string theory corrections to the supergravity action, including higher order terms with the Ramond-Ramond five-form field strength. We extend our previous results presented in arXiv:1110.0526. Photoemission rates depend on the 't Hooft coupling, and their curves suggest an interpolating behaviour from strong towards weak coupling regimes. Their slopes at zero light-like momentum give the electrical conductivity as a function of the 't Hooft coupling, in full agreement with our previous results of arXiv:1108.6306. Furthermore, we also study the effect of corrections beyond the large N limit.Comment: 36 pages, 5 figures, paragraph added in the conclusions, references added, typos correcte