Showing papers by "Ayan Mukhopadhyay published in 2011"

The unconditional RG flow of the relativistic holographic fluid

Abstract: We study asymptotically slowly varying perturbations of the AdS black brane in Einstein's gravity with a negative cosmological constant. We allow both the induced metric and the Brown-York stress tensor at a given radial cut-off slice to fluctuate. These fluctuations, which determine the radial evolution of the metric, are parametrized in terms of boundary data. We observe that the renormalized energy-momentum tensor at any radial slice takes the standard hydrodynamic form which is relativistically covariant with respect to the induced metric. The RG flow of the fluid takes the form of field redefinitions of the boundary hydrodynamic variables. To show this, up to first order in the derivative expansion, we only need to investigate the radial flow of the boundary data and do not need to impose constraints on them. Imposing the constraints gives unforced nonlinear hydrodynamic equations at any radial slice. Along the way we make a careful study of the choice of counter-terms and hypersurfaces involved in defining the holographic RG flow, while at the same time we do not explicitly set any boundary condition either at the cut-off or at the horizon. We find that \eta/s does not change along the RG flow, equaling 1/(4\pi) when the future horizon is regular. We also analyze the flow of the speed of sound and find that it diverges at the horizon.

The unconditional RG flow of the relativistic holographic fluid

Abstract: We study asymptotically slowly varying perturbations of the AdS black brane in Einstein’s gravity with a negative cosmological constant. We allow both the induced metric and the Brown-York stress tensor at a given radial cut-off slice to fluctuate. These fluctuations, which determine the radial evolution of the metric, are parametrized in terms of boundary data. We observe that the renormalized energy-momentum tensor at any radial slice takes the standard hydrodynamic form which is relativistically covariant with respect to the induced metric. The RG flow of the fluid takes the form of field redefinitions of the boundary hydrodynamic variables. To show this, up to first order in the derivative expansion, we only need to investigate the radial flow of the boundary data and do not need to impose constraints on them. Imposing the constraints gives unforced nonlinear hydrodynamic equations at any radial slice. Along the way we make a careful study of the choice of counter-terms and hypersurfaces involved in defining the holographic RG flow, while at the same time we do not explicitly set any boundary condition either at the cut-off or at the horizon. We find that η/s does not change along the RG flow, equaling 1/(4π) when the future horizon is regular. We also analyze the flow of the speed of sound and find that it diverges at the horizon.

Homogeneous relaxation at strong coupling from gravity

Abstract: Homogeneous relaxation is a ubiquitous phenomenon in semiclassical kinetic theories where the quasiparticles are distributed uniformly in space, and the equilibration involves only their velocity distribution. For such solutions, the hydrodynamic variables remain constant. We construct asymptotically AdS solutions of Einstein's gravity dual to such processes at strong coupling, perturbatively in the amplitude expansion, where the expansion parameter is the ratio of the amplitude of the non-hydrodynamic shear-stress tensor to the pressure. At each order, we sum over all time derivatives through exact recursion relations. We argue that the metric has a regular future horizon, order by order in the amplitude expansion, provided the shear-stress tensor follows an equation of motion. At the linear order, this equation of motion implies that the metric perturbations are composed of zero wavelength quasinormal modes. Our method allows us to calculate the non-linear corrections to this equation perturbatively in the amplitude expansion. We thus derive a special case of our previous conjecture on the regularity condition on the boundary stress tensor that endows the bulk metric with a regular future horizon, and also refine it further. We also propose a new outlook for heavy-ion phenomenology at RHIC and ALICE.

Phenomenology of irreversible processes from gravity

Abstract: Department of Physics and Astronomy, University of Southern CaliforniaLos Angeles, California 90089-0484,USAE-mail:ramaiyer@usc.eduWe propose that the space-time evolution of strongly coupled matter formed by ultra-relativisticheavy ion collisions can be modelled by phenomenological equations involving the energy-momentum tensor and conserved currents alone. These equations can describe the late stage oflocal thermal and chemical equilibration of the matter formed after collisions, and its subsequenttransition to hydrodynamic expansion in an unified framewor k. The full set of equations includelocal energy, momentum and charge conservation; but also additional equations for evolution ofnon-equilibrium variables. These equations with precisely determined phenomenological param-eters can be obtained by the AdS/CFT correspondence. On the gravity side of this correspon-dence, for vanishing chemical potentials, these phenomenological equations give all solutions ofpure gravity in AdS which have regular future horizons. We also discuss field-theoretic groundsfor validity of these phenomenological equations.The 2011 Europhysics Conference on High Energy Physics-HEP2011,July 21-27, 2011Grenoble, RhAt’ne-Alpes France

Phenomenology of Irreversible Processes from Gravity

Abstract: We propose that the space-time evolution of strongly coupled matter formed by ultra-relativistic heavy ion collisions can be modelled by phenomenological equations involving the energy-momentum tensor and conserved currents alone. These equations can describe the late stage of local chemical and thermal equilibration of the matter formed after collisions, and its subsequent transition to hydrodynamic expansion in an unified framework. The full set of equations include local energy, momentum and charge conservation; but also additional equations for evolution of non-equilibrium variables. These equations with precisely determined phenomenological parameters can be obtained by the AdS/CFT correspondence. On the gravity side of this correspondence, for vanishing chemical potentials, these phenomenological equations give all solutions of pure gravity in AdS which have regular future horizons. We also discuss field-theoretic grounds for validity of these phenomenological equations.