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55
Gravity & Hydrodynamics: Lectures on the fluidgravity correspondence
, 2009
"... We discuss recent developments in the hydrodynamic description of strongly coupled conformal field theories using the AdS/CFT correspondence. In particular, we review aspects of the fluidgravity correspondence which provides a map between a class of inhomogeneous, dynamical, black hole solutions in ..."
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We discuss recent developments in the hydrodynamic description of strongly coupled conformal field theories using the AdS/CFT correspondence. In particular, we review aspects of the fluidgravity correspondence which provides a map between a class of inhomogeneous, dynamical, black hole solutions in asymptotically AdS spacetimes and arbitrary fluid flows in the strongly interacting boundary field theory. We explain how the geometric duals to the fluid dynamics are constructed in a boundary derivative expansion and use the construction to extract the hydrodynamic transport coefficients. In addition we also describe the recent developments extending the correspondence to incorporate matter fields and to nonrelativistic systems. Based on
Relativistic Viscous Fluid Dynamics and NonEquilibrium Entropy
, 906
"... Abstract: Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains the most general (causal) equations of motion for a ..."
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Cited by 33 (2 self)
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Abstract: Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains the most general (causal) equations of motion for a fluid in the presence of shear and bulk viscosity, as well as the structure of the nonequilibrium entropy current. Requiring positivity of the divergence of the nonequilibrium entropy current relates some of its coefficients to those entering the equations of motion. I comment on possible
Domain Wall Holography for Finite Temperature Scaling Solutions
 JHEP
"... We investigate a class of nearextremal solutions of EinsteinMaxwellscalar theory with electric charge and power law scaling, dual to charged IR phases of relativistic field theories at low temperature. These are exact solutions of theories with domain wall vacua; hence, we use nonconformal hologr ..."
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Cited by 33 (1 self)
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We investigate a class of nearextremal solutions of EinsteinMaxwellscalar theory with electric charge and power law scaling, dual to charged IR phases of relativistic field theories at low temperature. These are exact solutions of theories with domain wall vacua; hence, we use nonconformal holography to relate the bulk and boundary theories. We numerically construct a global interpolating solution between the IR charged solutions and the UV domain wall vacua for arbitrary physical choices of Lagrangian parameters. By passing to a conformal frame in which the domain wall metric becomes that of AdS, we uncover a generalized scale invariance of the IR scaling solution, indicating a connection to the physics of Lifshitz fixed points. Finally, guided by effective field theoretic principles and the physics of nonconformal Dbranes, we argue for the applicability of domain wall holography even in theories with AdS critical points, namely those theories for which a scalar potential is dominated by a single exponential term over a large range.
Holography for chiral scaleinvariant models
 JHEP 1102 (2011) 082, arXiv:1010.4800 [hepth
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Sum Rules from an Extra Dimension
, 2010
"... Using the gravity side of the AdS/CFT correspondence, we investigate the analytic properties of thermal retarded Green’s functions for scalars, conserved currents, the stress tensor, and massless fermions. We provide some results concerning their large and small frequency behavior and their pole s ..."
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Cited by 14 (0 self)
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Using the gravity side of the AdS/CFT correspondence, we investigate the analytic properties of thermal retarded Green’s functions for scalars, conserved currents, the stress tensor, and massless fermions. We provide some results concerning their large and small frequency behavior and their pole structure. From these results, it is straightforward to prove the validity of various sum rules on the field theory side of the duality. We introduce a novel contraction mapping we use to study the large frequency behavior of the Green’s
Gauge/String Duality, Hot QCD and Heavy Ion Collisions
, 2014
"... Over the last decade, both experimental and theoretical advances have brought the need for strong coupling techniques in the analysis of deconfined QCD matter and heavy ion collisions to the forefront. As a consequence, a fruitful interplay has developed between analyses of stronglycoupled nonabel ..."
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Cited by 10 (0 self)
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Over the last decade, both experimental and theoretical advances have brought the need for strong coupling techniques in the analysis of deconfined QCD matter and heavy ion collisions to the forefront. As a consequence, a fruitful interplay has developed between analyses of stronglycoupled nonabelian plasmas via the gauge/string duality (also referred to as the AdS/CFT correspondence) and the phenomenology of heavy ion collisions. We review some of the main insights gained from this interplay to date. To establish a common language, we start with an introduction to heavy ion phenomenology and finitetemperature QCD, and a corresponding introduction to important concepts and techniques in the gauge/string duality. These introductory sections are written for nonspecialists, with the goal of bringing readers ranging from beginning graduate students to experienced practitioners of either QCD or gauge/string duality to the point that they understand enough about both fields that they can then appreciate their interplay in all appropriate contexts. We then review the current stateofthe art in the application of the duality to the description of the dynamics of strongly coupled plasmas, with emphases that include: its thermodynamic, hydrodynamic and transport properties; the way it both modifies the dynamics of, and is perturbed by, highenergy or heavy quarks passing through it; and the physics of quarkonium mesons within it. We seek throughout to stress the lessons that can be extracted from these computations for heavy ion physics as well as to discuss future directions and open problems for the field. ar X iv
A universal fermionic analogue of the shear viscosity
, 2013
"... We holographically compute supercharge diffusion constants in supersymmetric field theories, dual to AdS black brane solutions of arbitrary dimension. This includes the extension of earlier work by Kontoudi and Policastro for D3branes to M2 and M5brane theories. We consider the case of vanishing ..."
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Cited by 6 (0 self)
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We holographically compute supercharge diffusion constants in supersymmetric field theories, dual to AdS black brane solutions of arbitrary dimension. This includes the extension of earlier work by Kontoudi and Policastro for D3branes to M2 and M5brane theories. We consider the case of vanishing chemical potential. In particular, we relate the product of a diffusion constant and the energy density to a universal result for the fermionic absorption cross section. This relation is analogous to the famous proof of universality of η/s. We calculate the diffusion constants in two different ways: First, the computation is performed via the low frequency, low momentum pole of the correlator of supersymmetry currents. This pole describes the hydrodynamic phonino mode, the massless Goldstone fermion of spontaneous supersymmetry breaking by temperature. Second, the calculation is carried out using the dual transversal mode of the bulk gravitino, with the help of a new Kubo formula. Moreover, we provide some evidence for the applicability of generalized dimensional reduction for fermions when computing the corresponding Dpbrane diffusion constants.
The Fluid/Gravity Correspondence: a new perspective on the Membrane Paradigm
, 2011
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Holography and hydrodynamics for EMD theory with two Maxwell fields, JHEP 1303
, 2013
"... We use ‘generalized dimensional reduction ’ to relate a specific EinsteinMaxwellDilaton (EMD) theory, including two gauge fields, three neutral scalars and an axion, to higherdimensional AdS gravity (with no higherdimensional Maxwell field). In general, this is a dimensional reduction over compa ..."
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Cited by 6 (0 self)
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We use ‘generalized dimensional reduction ’ to relate a specific EinsteinMaxwellDilaton (EMD) theory, including two gauge fields, three neutral scalars and an axion, to higherdimensional AdS gravity (with no higherdimensional Maxwell field). In general, this is a dimensional reduction over compact Einstein spaces in which the dimension of the compact space is continued to nonintegral values. Specifically, we perform a nondiagonal KaluzaKlein (KK) reduction over a torus, involving two KK gauge fields. Our aim is to determine the holographic dictionary and hydrodynamic behaviour of the lowerdimensional theory by performing the generalized dimensional reduction on AdS. We study a specific example of a black brane carrying a wave, whose universal sector is described by gravity coupled to two Maxwell fields, three neutral scalars and an axion, and compute the first order transport coefficients of the dual theory. In these theories ζ̂s/η ̂ < 2 1/(d − 1) − ĉ2s, where ĉs is the speed of sound, violating a conjectured bound, but an alternative bound is satisfied. 1 ar