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73
A boundary stress tensor for higher-derivative gravity
- in AdS and Lifshitz backgrounds, JHEP 1004 (2010) 093, 1001.3598
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A Covariant Form of the Navier-Stokes Equation for the Galilean Conformal Algebra
, 908
"... We demonstrate that the Navier-Stokes equation can be covariantized under the full infinite dimensional Galilean Conformal Algebra (GCA), such that it reduces to the usual Navier-Stokes equation in an inertial frame. The covariantization is possible only for incompressible flows, i.e. when the diver ..."
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We demonstrate that the Navier-Stokes equation can be covariantized under the full infinite dimensional Galilean Conformal Algebra (GCA), such that it reduces to the usual Navier-Stokes equation in an inertial frame. The covariantization is possible only for incompressible flows, i.e. when the divergence of the velocity field vanishes. Using the continuity equation, we can fix the transformation of the pressure and density under GCA uniquely. We also find that when all chemical potentials vanish, cs, which denotes the speed of sound in an inertial frame comoving with the flow, must either be a fundamental constant or given in terms of microscopic parameters. We will discuss how both could be possible. In absence of chemical potentials, we also find that the covariance under GCA implies that either the viscosity should vanish or the microscopic theory should have a length scale or a time scale or both. We argue that we can be open to the later possibility. Finally, we see that the higher derivative corrections to the Naver-Stokes equation, can be covariantized, only if they are restricted to certain possible combinations in the inertial frame. We explicitly evaluate all possible three derivative corrections.
The Fluid/Gravity Correspondence: a new perspective on the Membrane Paradigm
, 2011
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Holographic Chiral Magnetic Conductivity
, 908
"... We present holographic computations of the time-dependent chiral magnetic conductivity in the framework of gauge/gravity correspondence. Chiral magnetic effect is a phenomenon where an electromagnetic current parallel to an applied magnetic field is induced in the presence of a finite axial chemical ..."
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We present holographic computations of the time-dependent chiral magnetic conductivity in the framework of gauge/gravity correspondence. Chiral magnetic effect is a phenomenon where an electromagnetic current parallel to an applied magnetic field is induced in the presence of a finite axial chemical potential. Motivated by a recent weak-coupling perturbative QCD calculation, our aim is to provide a couple of complementary computations for strongly coupled regime which might be relevant for strongly coupled RHIC plasma. We take two prototypical holographic set-ups for computing chiral magnetic conductivity; the first model is Einstein gravity with U(1)L × U(1)R Maxwell theory, and our second set-up is based on the Sakai-Sugimoto model in a deconfined and chiral symmetry restored phase. While the former takes into account full back-reaction while the latter not, the common feature is an important role played by the appropriate 5-dimensional Chern-Simons term corresponding to the 4-dimensional axial anomaly. 1
External Fields and the Dynamics of Fundamental Flavours IN HOLOGRAPHIC DUALS OF LARGE N GAUGE THEORIES
, 2010
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ELECTRIFIED PLASMA IN AdS/CFT CORRESPONDENCE
, 2010
"... We construct new gravity backgrounds holographic dual to neutral plasma with U(1) global symmetry in the presence of constant electric field, considering its full back-reactions to the metric. As the electric field and the induced current cause a net energy in-flow to the system, the plasma is conti ..."
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We construct new gravity backgrounds holographic dual to neutral plasma with U(1) global symmetry in the presence of constant electric field, considering its full back-reactions to the metric. As the electric field and the induced current cause a net energy in-flow to the system, the plasma is continually heated up and the corresponding gravity solution has an expanding horizon. After proposing a consistent late-time expansion scheme, we present analytic solutions in the scheme up to next-leading order, and our solutions are new time-dependent solutions of 5D asymptotic AdS Einstein-Maxwell(-Chern-Simons) theory. To extract dual CFT stress tensor and U(1) current from the solutions, we perform a rigorous holographic renormalization of Einstein-Maxwell-Chern-Simons theory including full back-reactions, which can in itself be an interesting addition to literatures. As by-products, we obtain interesting modifications of energy-momentum/current Ward identities due to the U(1) symmetry and its triangle anomaly. MIRAMARE – TRIESTE
From Navier-Stokes to Einstein
, 2011
"... 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 Σc wh ..."
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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 Σc whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a “near-horizon” limit in which Σc 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.
Phase diagram for non-axisymmetric plasma balls
, 910
"... Plasma balls and rings emerge as fluid holographic duals of black holes and black rings in the hydrodynamic/gravity correspondence for the Sherck-Schwarz AdS system. Recently, plasma balls spinning above a critical rotation were found to be unstable against m-lobed perturbations. In the phase diagra ..."
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Plasma balls and rings emerge as fluid holographic duals of black holes and black rings in the hydrodynamic/gravity correspondence for the Sherck-Schwarz AdS system. Recently, plasma balls spinning above a critical rotation were found to be unstable against m-lobed perturbations. In the phase diagram of stationary solutions the threshold of the instability signals a bifurcation to a new phase of non-axisymmetric configurations. We find explicitly this family of solutions and represent them in the phase diagram. We discuss the implications of our results for the gravitational system. Rotating non-axisymmetric black holes necessarily radiate gravitational waves. We thus emphasize that it would be important, albeit possibly out of present reach, to have a better understanding of the hydrodynamic description of gravitational waves and of the gravitational interaction between two bodies. We also argue that it might well be that a non-axisymmetric m-lobed instability is also present in Myers-Perry black holes for rotations below the recently found ultraspinning instability. Contents
An AdS/CFT Connection between Boltzmann and Einstein
- Phys.Rev. D81 (2010) 086005, arXiv:0907.1156 [hep-th
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