New stability results for Einstein scalar gravity

We consider asymptotically anti de Sitter gravity coupled to a scalar field with mass slightly above the Breitenlohner-Freedman bound. This theory admits a large class of consistent boundary conditions characterized by an arbitrary function $W$. An important open question is to determine which $W$ admit stable ground states. It has previously been shown that the total energy is bounded from below if $W$ is bounded from below and the bulk scalar potential $V(\phi)$ admits a suitable superpotential. We extend this result and show that the energy remains bounded even in some cases where $W$ can become arbitrarily negative. As one application, this leads to the possibility that in gauge/gravity duality, one can add a double trace operator with negative coefficient to the dual field theory and still have a stable vacuum

Towards a Non-Relativistic Holographic Superfluid

We explore the phase structure of a holographic toy model of superfluid states in non-relativistic conformal field theories. At low background mass density, we find a familiar second-order transition to a superfluid phase at finite temperature. Increasing the chemical potential for the probe charge density drives this transition strongly first order as the low-temperature superfluid phase merges with a thermodynamically disfavored high-temperature condensed phase. At high background mass density, the system reenters the normal phase as the temperature is lowered further, hinting at a zero-temperature quantum phase transition as the background density is varied. Given the unusual thermodynamics of the background black hole, however, it seems likely that the true ground state is another configuration altogether.Comment: 13+5 pages, late

Large-density field theory, viscosity, and "2kF2k_F" singularities from string duals

We analyze systems where an effective large-N expansion arises naturally in gauge theories without a large number of colors: a sufficiently large charge density alone can produce a perturbative string ('tHooft) expansion. One example is simply the well-known NS5/F1 system dual to $AdS_3\times T^4\times S^3$, here viewed as a 5+1 dimensional theory at finite density. This model is completely stable, and we find that the existing string-theoretic solution of this model yields two interesting results. First, it indicates that the shear viscosity is not corrected by $\alpha'$ effects in this system. For flow perpendicular to the F1 strings the viscosity to entropy ratio take the usual value $1/4\pi$, but for flow parallel to the F1's it vanishes as $T^2$ at low temperature. Secondly, it encodes singularities in correlation functions coming from low-frequency modes at a finite value of the momentum along the $T^4$ directions. This may provide a strong coupling analogue of finite density condensed matter systems for which fermionic constituents of larger operators contribute so-called "$2k_F$" singularities. In the NS5/F1 example, stretched strings on the gravity side play the role of these composite operators. We explore the analogue for our system of the Luttinger relation between charge density and the volume bounded by these singular surfaces. This model provides a clean example where the string-theoretic UV completion of the gravity dual to a finite density field theory plays a significant and calculable role.Comment: 28 pages. v2: added reference

Luttinger's theorem, superfluid vortices, and holography

Strongly coupled field theories with gravity duals can be placed at finite density in two ways: electric field flux emanating from behind a horizon, or bulk charged fields outside of the horizon that explicitly source the density. We discuss field-theoretical observables that are sensitive to this distinction. If the charged fields are fermionic, we discuss a modified Luttinger's theorem that holds for holographic systems, in which the sum of boundary theory Fermi surfaces counts only the charge outside of the horizon. If the charged fields are bosonic, we show that the the resulting superfluid phase may be characterized by the coefficient of the transverse Magnus force on a moving superfluid vortex, which again is sensitive only to the charge outside of the horizon. For holographic systems these observables provide a field-theoretical way to distinguish how much charge is held by a dual horizon, but they may be useful in more general contexts as measures of deconfined (i.e. "fractionalized") charge degrees of freedom.Comment: 21 pages; version 2: minor changes, version to be published in CQG; version 3: minor change

Semi-local quantum liquids

Gauge/gravity duality applied to strongly interacting systems at finite density predicts a universal intermediate energy phase to which we refer as a semi-local quantum liquid. Such a phase is characterized by a finite spatial correlation length, but an infinite correlation time and associated nontrivial scaling behavior in the time direction, as well as a nonzero entropy density. For a holographic system at a nonzero chemical potential, this unstable phase sets in at an energy scale of order of the chemical potential, and orders at lower energies into other phases; examples include superconductors and antiferromagnetic-type states. In this paper we give examples in which it also orders into Fermi liquids of "heavy" fermions. While the precise nature of the lower energy state depends on the specific dynamics of the individual system, we argue that the semi-local quantum liquid emerges universally at intermediate energies through deconfinement (or equivalently fractionalization). We also discuss the possible relevance of such a semi-local quantum liquid to heavy electron systems and the strange metal phase of high temperature cuprate superconductors.Comment: 31 pages, 7 figure

Fractionalization of holographic Fermi surfaces

Zero temperature states of matter are holographically described by a spacetime with an asymptotic electric flux. This flux can be sourced either by explicit charged matter fields in the bulk, by an extremal black hole horizon, or by a combination of the two. We refer to these as mesonic, fully fractionalized and partially fractionalized phases of matter, respectively. By coupling a charged fluid of fermions to an asymptotically AdS_4 Einstein-Maxwell-dilaton theory, we exhibit quantum phase transitions between all three of these phases. The onset of fractionalization can be either a first order or continuous phase transition. In the latter case, at the quantum critical point the theory displays an emergent Lifshitz scaling symmetry in the IR.Comment: 1+24 pages. 7 figure

Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality

Strongly correlated quantum fluids are phases of matter that are intrinsically quantum mechanical, and that do not have a simple description in terms of weakly interacting quasi-particles. Two systems that have recently attracted a great deal of interest are the quark-gluon plasma, a plasma of strongly interacting quarks and gluons produced in relativistic heavy ion collisions, and ultracold atomic Fermi gases, very dilute clouds of atomic gases confined in optical or magnetic traps. These systems differ by more than 20 orders of magnitude in temperature, but they were shown to exhibit very similar hydrodynamic flow. In particular, both fluids exhibit a robustly low shear viscosity to entropy density ratio which is characteristic of quantum fluids described by holographic duality, a mapping from strongly correlated quantum field theories to weakly curved higher dimensional classical gravity. This review explores the connection between these fields, and it also serves as an introduction to the Focus Issue of New Journal of Physics on Strongly Correlated Quantum Fluids: from Ultracold Quantum Gases to QCD Plasmas. The presentation is made accessible to the general physics reader and includes discussions of the latest research developments in all three areas.Comment: 138 pages, 25 figures, review associated with New Journal of Physics special issue "Focus on Strongly Correlated Quantum Fluids: from Ultracold Quantum Gases to QCD Plasmas" (http://iopscience.iop.org/1367-2630/focus/Focus%20on%20Strongly%20Correlated%20Quantum%20Fluids%20-%20from%20Ultracold%20Quantum%20Gases%20to%20QCD%20Plasmas