Holographic bulk viscosity: GPR vs EO

Recently Eling and Oz (EO) proposed a formula for the holographic bulk viscosity, in arXiv:1103.1657, derived from the null horizon focusing equation. This formula seems different from that obtained earlier by Gubser, Pufu and Rocha (GPR) in arXiv:0806.0407 calculated from the IR limit of the two-point function of the trace of the stress tensor. The two were shown to agree only for some simple scaling cases. We point out that the two formulae agree in two non-trivial holographic theories describing RG flows. The first is the strongly coupled N=2* gauge theory plasma. The second is the semi-phenomenological model of Improved Holographic QCD.Comment: 21 pages, 2 figure

Continuous Hawking-Page transitions in Einstein-scalar gravity

We investigate continuous Hawking-Page transitions in Einstein's gravity coupled to a scalar field with an arbitrary potential in the weak gravity limit. We show that this is only possible in a singular limit where the black-hole horizon marginally traps a curvature singularity. Depending on the subleading terms in the potential, a rich variety of continuous phase transitions arise. Our examples include second and higher order, including the Berezinskii-Kosterlitz-Thouless type. In the case when the scalar is dilaton, the condition for a continuous phase transition lead to (asymptotically) linear-dilaton background. We obtain the scaling laws of thermodynamic functions, as well as the viscosity coefficients near the transition. In the limit of weak gravitational interactions, the bulk viscosity asymptotes to a universal constant, independent of the details of the scalar potential. As a byproduct of our analysis we obtain a one-parameter family of kink solutions in arbitrary dimension d that interpolate between AdS near the boundary and linear-dilaton background in the deep interior. The continuous Hawking-Page transitions found here serve as holographic models for normal-to superfluid transitions.Comment: 35 pages + appendice

Gravitational collapse and thermalization in the hard wall model

We study a simple example of holographic thermalization in a confining field theory: the homogeneous injection of energy in the hard wall model. Working in an amplitude expansion, we find black brane formation for sufficiently fast energy injection and a scattering wave solution for sufficiently slow injection. We comment on our expectations for more sophisticated holographic QCD models.Comment: 33 pages, 5 figure

Holographic spin liquids and Lovelock Chern-Simons gravity

We explore the role of torsion as source of spin current in strongly interacting conformal fluids using holography. We establish the constitutive relations of the basic hydrodynamic variables, the energy-momentum tensor and the spin current based on the classification of the spin sources in irreducible Lorentz representations. The fluids we consider are assumed to be described by the five dimensional Lovelock-Chern-Simons gravity with independent vielbein and spin connection. We construct a hydrodynamic expansion that involves the stress tensor and the spin current and compute the corresponding one-point functions holographically. As a byproduct we find a class of interesting analytic solutions to the Lovelock-Chern-Simons gravity, including blackholes, by mapping the equations of motion into non-linear algebraic constraints for the sources. We also derive a Lee-Wald entropy formula for these blackholes in Chern-Simons theories with torsion. The blackhole solutions determine the thermodynamic potentials and the hydrodynamic constitutive relations in the corresponding fluid on the boundary. We observe novel spin induced transport in these holographic models: a dynamical version of the Barnett effect where vorticity generates a spin current and anomalous vortical transport transverse to a vector-like spin source.Comment: 52 page

The holographic quantum effective potential at finite temperature and density

We develop a formalism that allows the computation of the quantum effective potential of a scalar order parameter in a class of holographic theories at finite temperature and charge density. The effective potential is a valuable tool for studying the ground state of the theory, symmetry breaking patterns and phase transitions. We derive general formulae for the effective potential and apply them to determine the phase transition temperature and density in the scaling region.Comment: 27 page

Deconfinement and Thermodynamics in 5D Holographic Models of QCD

We review 5D holographic approaches to finite temperature QCD. Thermodynamic properties of the "hard-wall" and the "soft-wall" models are derived. Various non-realistic features in these models are cured by the set-up of improved holographic QCD, that we review here.Comment: Invited review paper for Mod. Phys. Let

Holography and Thermodynamics of 5D Dilaton-gravity

The asymptotically-logarithmically-AdS black-hole solutions of 5D dilaton gravity with a monotonic dilaton potential are analyzed in detail. Such theories are holographically very close to pure Yang-Mills theory in four dimensions. The existence and uniqueness of black-hole solutions is shown. It is also shown that a Hawking-Page transition exists at finite temperature if and only if the potential corresponds to a confining theory. The physics of the transition matches in detail with that of deconfinement of the Yang-Mills theory. The high-temperature phase asymptotes to a free gluon gas at high temperature matching the expected behavior from asymptotic freedom. The thermal gluon condensate is calculated and shown to be crucial for the existence of a non-trivial deconfining transition. The condensate of the topological charge is shown to vanish in the deconfined phase.Comment: LaTeX, 61 pages (main body) + 58 pages (appendix), 25 eps figures. Revised version, published in JHEP. Two equations added in Section 7.4; typos corrected; references adde

Holographic Conformal Window - A Bottom Up Approach

We propose a five-dimensional framework for modeling the background geometry associated to ordinary Yang-Mills (YM) as well as to nonsupersymmetric gauge theories possessing an infrared fixed point with fermions in various representations of the underlying gauge group. The model is based on the improved holographic approach, on the string theory side, and on the conjectured all-orders beta function for the gauge theory one. We first analyze the YM gauge theory. We then investigate the effects of adding flavors and show that, in the holographic description of the conformal window, the geometry becomes AdS when approaching the ultraviolet and the infrared regimes. As the number of flavors increases within the conformal window we observe that the geometry becomes more and more of AdS type over the entire energy range.Comment: 20 Pages, 3 Figures. v2: references adde

On the Temperature Dependence of the Shear Viscosity and Holography

We examine the structure of the shear viscosity to entropy density ratio eta/s in holographic theories of gravity coupled to a scalar field, in the presence of higher derivative corrections. Thanks to a non-trivial scalar field profile, eta/s in this setup generically runs as a function of temperature. In particular, its temperature behavior is dictated by the shape of the scalar potential and of the scalar couplings to the higher derivative terms. We consider a number of dilatonic setups, but focus mostly on phenomenological models that are QCD-like. We determine the geometric conditions needed to identify local and global minima for eta/s as a function of temperature, which translate to restrictions on the signs and ranges of the higher derivative couplings. Finally, such restrictions lead to an holographic argument for the existence of a global minimum for eta/s in these models, at or above the deconfinement transition.Comment: references adde