Zero Sound in Strange Metallic Holography

One way to model the strange metal phase of certain materials is via a holographic description in terms of probe D-branes in a Lifshitz spacetime, characterised by a dynamical exponent z. The background geometry is dual to a strongly-interacting quantum critical theory while the probe D-branes are dual to a finite density of charge carriers that can exhibit the characteristic properties of strange metals. We compute holographically the low-frequency and low-momentum form of the charge density and current retarded Green's functions in these systems for massless charge carriers. The results reveal a quasi-particle excitation when z<2, which in analogy with Landau Fermi liquids we call zero sound. The real part of the dispersion relation depends on momentum k linearly, while the imaginary part goes as k^2/z. When z is greater than or equal to 2 the zero sound is not a well-defined quasi-particle. We also compute the frequency-dependent conductivity in arbitrary spacetime dimensions. Using that as a measure of the charge current spectral function, we find that the zero sound appears only when the spectral function consists of a single delta function at zero frequency.Comment: 20 pages, v2 minor corrections, extended discussion in sections 5 and 6, added one footnote and four references, version published in JHE

Towards strange metallic holography

We initiate a holographic model building approach to `strange metallic' phenomenology. Our model couples a neutral Lifshitz-invariant quantum critical theory, dual to a bulk gravitational background, to a finite density of gapped probe charge carriers, dually described by D-branes. In the physical regime of temperature much lower than the charge density and gap, we exhibit anomalous scalings of the temperature and frequency dependent conductivity. Choosing the dynamical critical exponent $z$ appropriately we can match the non-Fermi liquid scalings, such as linear resistivity, observed in strange metal regimes. As part of our investigation we outline three distinct string theory realizations of Lifshitz geometries: from F theory, from polarised branes, and from a gravitating charged Fermi gas. We also identify general features of renormalisation group flow in Lifshitz theories, such as the appearance of relevant charge-charge interactions when $z \geq 2$. We outline a program to extend this model building approach to other anomalous observables of interest such as the Hall conductivity.Comment: 71 pages, 8 figure

Novel Solutions of Finite-Density D3/D5 Probe Brane System and Their Implications for Stability

In this article we present a novel set of solutions of the probe brane system consisting of Nf-D5 probe branes embedded in the near-horizon geometry generated by Nc-D3 branes, with the D5 worldvolume U(1) gauge fields turned on. Our system is holographically dual to a supersymmetric defect field theory at finite density in non-trivial vacua. We find that a large class of vacua turns out to satisfy a no-force condition, even with supersymmetry explicitly broken by the finite density; our solutions include configuration in which charge separates from the horizon and is instead carried by probe branes outside the horizon. The free energy is lowered in this process. Whether this corresponds to a genuine instability of the finite-density probe brane system remains to be seen.Comment: 11 pages, 1 figure

Zero Sound in Effective Holographic Theories

We investigate zero sound in $D$-dimensional effective holographic theories, whose action is given by Einstein-Maxwell-Dilaton terms. The bulk spacetimes include both zero temperature backgrounds with anisotropic scaling symmetry and their near-extremal counterparts obtained in 1006.2124 [hep-th], while the massless charge carriers are described by probe D-branes. We discuss thermodynamics of the probe D-branes analytically. In particular, we clarify the conditions under which the specific heat is linear in the temperature, which is a characteristic feature of Fermi liquids. We also compute the retarded Green's functions in the limit of low frequency and low momentum and find quasi-particle excitations in certain regime of the parameters. The retarded Green's functions are plotted at specific values of parameters in $D=4$, where the specific heat is linear in the temperature and the quasi-particle excitation exists. We also calculate the AC conductivity in $D$-dimensions as a by-product.Comment: 29 pages, 1 figur

Probes on D3-D7 Quark-Gluon Plasmas

We study the holographic dual model of quenched flavors immersed in a quark-gluon plasma with massless dynamical quarks in the Veneziano limit. This is modeled by embedding a probe D7 brane in a background where the backreaction of massless D7 branes has been taken into account. The background, and hence the effects, are perturbative in the Veneziano parameter N_f/N_c, therefore giving small shifts of all magnitudes like the constituent mass, the quark condensate, and several transport coefficients. We provide qualitative results for the effect of flavor degrees of freedom on the probes. For example, the meson melting temperature is enhanced, while the screening length is diminished. The drag force is also enhanced.Comment: 31 pages, 17 figure

Thermodynamics of Holographic Defects

Using the AdS/CFT correspondence, we study the thermodynamic properties and the phase diagram of matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional N=4 SYM "heat bath". Considering a background magnetic field, (net) quark density, defect "magnitude" $\delta N_c$ and the mass of the matter, we study the defect contribution to the thermodynamic potentials and their first and second derivatives to map the phases and study their physical properties. We find some features that are qualitatively similar to other systems e.g. in (3+1) dimensions and a number of features that are particular to the defect nature, such as its magnetic properties, unexpected properties at T->0 and finite density; and the finite $\delta N_c$ effects, e.g. a diverging susceptibility and vanishing density of states at small temperatures, a physically consistent negative heat capacity and new types of consistent phases.Comment: 33 pages, 16 figures (jpg and pdf), typos fixed and references added, final version published in JHE

Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT

We present holographic descriptions of thermalization in conformal field theories using probe D-branes in AdS X S space-times. We find that the induced metrics on Dp-brane worldvolumes which are rotating in an internal sphere direction have horizons with characteristic Hawking temperatures even if there is no black hole in the bulk AdS. The AdS/CFT correspondence applied to such systems indeed reveals thermal properties such as Brownian motions and AC conductivities in the dual conformal field theories. We also use this framework to holographically analyze time-dependent systems undergoing a quantum quench, where parameters in quantum field theories, such as a mass or a coupling constant, are suddenly changed. We confirm that this leads to thermal behavior by demonstrating the formation of apparent horizons in the induced metric after a certain time.Comment: LaTeX, 47 pages, 14 figures; Typos corrected and references added (v2); minor corrections, references added(v3

Baryon charge from embedding topology and a continuous meson spectrum in a new holographic gauge theory

We study a new holographic gauge theory based on probe D4-branes in the background dual to D4-branes on a circle with antiperiodic boundary conditions for fermions. Field theory configurations with baryons correspond to smooth embeddings of the probe D4-branes with nontrivial winding around an S^4 in the geometry. As a consequence, physics of baryons and nuclei can be studied reliably in this model using the abelian Born-Infeld action. However, surprisingly, we find that the meson spectrum is not discrete. This is related to a curious result that the action governing small fluctuations of the gauge field on the probe brane is the five-dimensional Maxwell action in Minkowski space despite the non-trivial embedding of the probe brane in the curved background geometry.Comment: 24 pages, LaTeX, 10 figures, v4: previously ignored effects of coupling to RR-fields included, meson spectrum qualitatively changed, v5: journal versio

Holographic Conductivity in Disordered Systems

The main purpose of this paper is to holographically study the behavior of conductivity in 2+1 dimensional disordered systems. We analyze probe D-brane systems in AdS/CFT with random closed string and open string background fields. We give a prescription of calculating the DC conductivity holographically in disordered systems. In particular, we find an analytical formula of the conductivity in the presence of codimension one randomness. We also systematically study the AC conductivity in various probe brane setups without disorder and find analogues of Mott insulators.Comment: 43 pages, 28 figures, latex, references added, minor correction

Heavy quark density in N=4 SYM: from hedgehog to Lifshitz spacetimes

We study the effect of an order N^2 density of heavy quarks in strongly coupled N=4 SUSY Yang-Mills theory in the large N limit. This is achieved in the type IIB supergravity dual by introducing a uniformly smeared density of macroscopic string sources stretching to the boundary of AdS_5 x S^5. The backreacted system exhibits a flow from an AdS_5 "hedgehog" geometry to a scaling Lifshitz-like solution Lif_5 x S^5 with dynamical critical exponent z=7, wherein the scaling symmetry is broken by a logarithmic running dilaton. We find an exact black brane solution within the scaling regime which describes the low temperature thermodynamics of the system.Comment: 20 pages, 2 figures, references adde