Holography, Fractionalization and Magnetic Fields

Four dimensional gravity with a U(1) gauge field, coupled to various fields in asymptotically anti-de Sitter spacetime, provides a rich arena for the holographic study of the strongly coupled (2+1)-dimensional dynamics of finite density matter charged under a global U(1). As a first step in furthering the study of the properties of fractionalized and partially fractionalized degrees of freedom in the strongly coupled theory, we construct electron star solutions at zero temperature in the presence of a background magnetic field. We work in Einstein-Maxwell-dilaton theory. In all cases we construct, the magnetic source is cloaked by an event horizon. A key ingredient of our solutions is our observation that starting with the standard Landau level structure for the density of states, the electron star limits reduce the charge density and energy density to that of the free fermion result. Using this result we construct three types of solution: One has a star in the infra-red with an electrically neutral horizon, another has a star that begins at an electrically charged event horizon, and another has the star begin a finite distance from an electrically charged horizon.Comment: 18 pages, 2 figures. Submitted to Springer Lecture Notes: Strongly interacting matter in magnetic fields. v2: Updated references and adjusted some phrasing in the introductio

Universal scaling properties of extremal cohesive holographic phases

We show that strongly-coupled, translation-invariant holographic IR phases at finite density can be classified according to the scaling behaviour of the metric, the electric potential and the electric flux introducing four critical exponents, independently of the details of the setup. Solutions fall into two classes, depending on whether they break relativistic symmetry or not. The critical exponents determine key properties of these phases, like thermodynamic stability, the (ir)relevant deformations around them, the low-frequency scaling of the optical conductivity and the nature of the spectrum for electric perturbations. We also study the scaling behaviour of the electric flux through bulk minimal surfaces using the Hartnoll-Radicevic order parameter, and characterize the deviation from the Ryu-Takayanagi prescription in terms of the critical exponents.Comment: v4: corrected a typo in eqn (3.29), now (3.28). Conclusions unchange

The Spin of Holographic Electrons at Nonzero Density and Temperature

We study the Green's function of a gauge invariant fermionic operator in a strongly coupled field theory at nonzero temperature and density using a dual gravity description. The gravity model contains a charged black hole in four dimensional anti-de Sitter space and probe charged fermions. In particular, we consider the effects of the spin of these probe fermions on the properties of the Green's function. There exists a spin-orbit coupling between the spin of an electron and the electric field of a Reissner-Nordstrom black hole. On the field theory side, this coupling leads to a Rashba like dispersion relation. We also study the effects of spin on the damping term in the dispersion relation by considering how the spin affects the placement of the fermionic quasinormal modes in the complex frequency plane in a WKB limit. An appendix contains some exact solutions of the Dirac equation in terms of Heun polynomials.Comment: 27 pages, 11 figures; v2: minor changes, published versio

Aspects of holography for theories with hyperscaling violation

We analyze various aspects of the recently proposed holographic theories with general dynamical critical exponent z and hyperscaling violation exponent $\theta$. We first find the basic constraints on $z, \theta$ from the gravity side, and compute the stress-energy tensor expectation values and scalar two-point functions. Massive correlators exhibit a nontrivial exponential behavior at long distances, controlled by $\theta$. At short distance, the two-point functions become power-law, with a universal form for $\theta > 0$. Next, the calculation of the holographic entanglement entropy reveals the existence of novel phases which violate the area law. The entropy in these phases has a behavior that interpolates between that of a Fermi surface and that exhibited by systems with extensive entanglement entropy. Finally, we describe microscopic embeddings of some $\theta \neq 0$ metrics into full string theory models -- these metrics characterize large regions of the parameter space of Dp-brane metrics for $p\neq 3$. For instance, the theory of N D2-branes in IIA supergravity has z=1 and $\theta = -1/3$ over a wide range of scales, at large $g_s N$.Comment: 35 pages; v2: new references added; v3: proper reference [14] added; v4: minor clarification

Stellar spectroscopy: Fermions and holographic Lifshitz criticality

Electron stars are fluids of charged fermions in Anti-de Sitter spacetime. They are candidate holographic duals for gauge theories at finite charge density and exhibit emergent Lifshitz scaling at low energies. This paper computes in detail the field theory Green's function G^R(w,k) of the gauge-invariant fermionic operators making up the star. The Green's function contains a large number of closely spaced Fermi surfaces, the volumes of which add up to the total charge density in accordance with the Luttinger count. Excitations of the Fermi surfaces are long lived for w <~ k^z. Beyond w ~ k^z the fermionic quasiparticles dissipate strongly into the critical Lifshitz sector. Fermions near this critical dispersion relation give interesting contributions to the optical conductivity.Comment: 38 pages + appendices. 9 figure

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

Lifshitz-like space-time from intersecting branes in string/M theory

We construct 1/4 BPS, threshold F-D$p$ bound states (with $0\leq p \leq 5$) of type II string theories by applying S- and T-dualities to the D1-D5 system of type IIB string theory. These are different from the known 1/2 BPS, non-threshold F-D$p$ bound states. The near horizon limits of these solutions yield Lifshitz-like space-times with varying dynamical critical exponent $z=2(5-p)/(4-p)$, for $p\neq 4$, along with the hyperscaling violation exponent $\theta = p - (p-2)/(4-p)$, showing how Lifshitz-like space-time can be obtained from string theory. The dilatons are in general non-constant (except for $p=1$). We discuss the holographic RG flows and the phase structures of these solutions. For $p=4$, we do not get a Lifshitz-like space-time, but the near horizon limit in this case leads to an AdS$_2$ space.Comment: 20 pages, no figure, v2: proper identification of hyperscaling violation exponent has been made, abstract and the text has been changed accordingly, note added, v3: minor changes, refs added, version to appear in JHE

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