Lifshitz Scaling Research Articles

Hyperscaling violation: a unified frame for effective holographic theories

We investigate systematic classifications of low energy and lower dimensional effective holographic theories with Lifshitz and Schr\"odinger scaling symmetries only using metrics in terms of hyperscaling violation ($\theta$) and dynamical ($z$) exponents. Their consistent parameter spaces are constrained by null energy and positive specific heat conditions, whose validity is explicitly checked against a previously known result. From dimensional reductions of many microscopic string solutions, we observe the classifications are tied with the number of scales in the original microscopic theories. Conformal theories do not generate a nontrivial $\theta$ for a simple sphere reduction. Theories with Lifshitz scaling with one scale are completely fixed by $\theta$ and $z$, and have a universal emblackening factor at finite temperature. Dimensional reduction of intersecting M2-M5 requires, we call, spatial anisotropic exponents ($\sharp$), along with $z$=1, $\theta$=0, because of another scale. Theories with Schr\"odinger scaling show similar simple classifications at zero temperature, while require more care due to an additional parameter being a thermodynamic variable at finite temperature.

Intersecting D-branes and Lifshitz-like space-time

In a previous paper [P. Dey and S. Roy, J. High Energy Phys. 06 (2012) 129] we have shown how Lifshitz-like space-times (space-times having Lifshitz scaling with hyperscaling violation) arise from $1/4$ Bogomol'nyi-Prasad-Sommerfield, threshold $\mathrm{F}\ensuremath{-}\mathrm{D}p$--bound state solutions of type II string theories in the near horizon limit. In this paper we show that similar structures also arise from the near horizon limit of $1/4$ Bogomol'nyi-Prasad-Sommerfield, threshold-intersecting D-brane solutions of type II string theories. Some of these solutions are standard ($\mathrm{D}p\ensuremath{-}\mathrm{D}(p+4)$ for $p=0$, 2) and some are nonstandard ($\mathrm{D}p\ensuremath{-}\mathrm{D}(p+2)$ for $p=1$, 2, 3), including $\mathrm{D}2\ensuremath{-}\mathrm{D}{2}^{\ensuremath{'}}$, $\mathrm{D}3\ensuremath{-}\mathrm{D}{3}^{\ensuremath{'}}$, and $\mathrm{D}4\ensuremath{-}\mathrm{D}{4}^{\ensuremath{'}}$ solutions. The dilatons of these solutions, in general, run (except in D2-D4 and $\mathrm{D}3\ensuremath{-}\mathrm{D}{3}^{\ensuremath{'}}$ cases) and produce renormalization group flows. We discuss the phase structures of these solutions. D2-D4 and $\mathrm{D}3\ensuremath{-}\mathrm{D}{3}^{\ensuremath{'}}$ in the near horizon limit do not produce Lifshitz-like space-time but give ${\mathrm{AdS}}_{3}$ spaces.

Thermal correlators in holographic models with Lifshitz scaling

We study finite temperature effects in two distinct holographic models that exhibit Lifshitz scaling, looking to identify model independent features in the dual strong coupling physics. We consider the thermodynamics of black branes and find different low-temperature behavior of the specific heat. Deformation away from criticality leads to non-trivial temperature dependence of correlation functions and we study how the characteristic length scale in the two point function of scalar operators varies as a function of temperature and deformation parameters.

Fractionalization of holographic Fermi surfaces

Zero temperature states of matter at finite charge density 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 AdS4 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.

On the True Nature of Renormalizability in Horava-Lifshitz Gravity

We argue that the true nature of the renormalizability of Horava-Lifshitz gravity lies in the presence of higher order spatial derivatives and not in the anisotropic Lifshitz scaling of space and time. We discuss the possibility of constructing a higher order spatial derivatives model that has the same renormalization properties of Horava-Lifshitz gravity but that does not make use of the Lifshitz scaling. In addition, the state-of-the-art of the Lorentz symmetry restoration in Horava-Lifshitz-type theories of gravitation is reviewed.

Deformations of Lifshitz holography in (n+1)-dimensions

We investigate deformations of Lifshitz holography in (n+1) dimensional spacetime. After discussing the situation for general Lifshitz scaling symmetry parameter z, we consider z = n−1 and the associated marginally relevant operators. These operators are dynamically generated by a momentum scale Λ ~ 0 and correspond to slightly deformed Lifshitz spacetimes via a holographic picture. We obtain renormalization group flow at finite temperature from UV Lifshitz to IR AdS, and evaluate how physical quantities such as the free energy density and the energy density depend on log(Λ z /T ) in the quantum critical regime as Λ z /T → 0.

Lifshitz scaling and hyperscaling violation in string theory

We explore string and $M$-theory constructions of holographic theories with Lifshitz scaling exponent $z$ and hyperscaling violation exponent $\ensuremath{\theta}$, finding a range of $z$, $\ensuremath{\theta}$ values. Some of these arise as effective metrics from dimensional reduction of certain kinds of null deformations of AdS spacetimes appearing in the near-horizon geometries of extremal D3-, M2-, and M5-brane theories. The ${\mathrm{AdS}}_{5}$ solution, in particular, gives rise to $\ensuremath{\theta}=1$ in $d=2$ (boundary) space dimensions. Other solutions arise as the IIA D2- and D4-brane solutions with appropriate null deformations, and we discuss the phase structure of these systems.

Lifshitz solitons

We numerically obtain a class of soliton solutions for Einstein gravity in ($n+1$) dimensions coupled to massive Abelian gauge fields and with a negative cosmological constant with Lifshitz asymptotic behavior. We find that for all $n\ensuremath{\ge}3$, a discrete set of magic values for the charge density at the origin (guaranteeing an asymptotically Lifshitz geometry) exists when the critical exponent associated with the Lifshitz scaling is $z=2$; moreover, in all cases, a single magic value is obtained for essentially every $1<z<2$, yet none when $z>2$ sufficiently.

Stability of Hořava-Lifshitz black holes in the context of AdS/CFT

The anti--de Sitter/conformal field theory (AdS/CFT) correspondence is a powerful tool that promises to provide new insights toward a full understanding of field theories under extreme conditions, including but not limited to quark-gluon plasma, Fermi liquid and superconductor. In many such applications, one typically models the field theory with asymptotically AdS black holes. These black holes are subjected to stringy effects that might render them unstable. Ho\v{r}ava-Lifshitz gravity, in which space and time undergo different transformations, has attracted attentions due to its power-counting renormalizability. In terms of AdS/CFT correspondence, Ho\v{r}ava-Lifshitz black holes might be useful to model holographic superconductors with Lifshitz scaling symmetry. It is thus interesting to study the stringy stability of Ho\v{r}ava-Lifshitz black holes in the context of AdS/CFT. We find that uncharged topological black holes in $\lambda=1$ Ho\v{r}ava-Lifshitz theory are nonperturbatively stable, unlike their counterparts in Einstein gravity, with the possible exceptions of negatively curved black holes with detailed balance parameter $\epsilon$ close to unity. Sufficiently charged flat black holes for $\epsilon$ close to unity, and sufficiently charged positively curved black holes with $\epsilon$ close to zero, are also unstable. The implication to the Ho\v{r}ava-Lifshitz holographic superconductor is discussed.

Gauss-Bonnet black holes and heavy fermion metals

We consider charged black holes in Einstein-Gauss-Bonnet Gravity with Lifshitz boundary conditions. We find that this class of models can reproduce the anomalous specific heat of condensed matter systems exhibiting non-Fermi-liquid behaviour at low temperatures. We find that the temperature dependence of the Sommerfeld ratio is sensitive to the choice of Gauss-Bonnet coupling parameter for a given value of the Lifshitz scaling parameter. We propose that this class of models is dual to a class of models of non-Fermi-liquid systems proposed by Castro-Neto et.al.

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.

Causality and Lifshitz Holography

We study signal propagation in theories with Lifshitz scaling using the gravity dual and show that backgrounds with z 1 are incompatible with causality of the strongly coupled theory. We argue that causality violations in z 1 theories show up in boundary correlation functions as superluminal modes.

Holographic entanglement entropy: near horizon geometry and disconnected regions

We study the finite term of the holographic entanglement entropy for the charged black hole in AdS(d+2) and other examples of black holes when the spatial region in the boundary theory is given by one or two parallel strips. For one large strip it scales like the width of the strip. The divergent term of its expansion as the turning point of the minimal surface approaches the horizon is determined by the near horizon geometry. Examples involving a Lifshitz scaling are also considered. For two equal strips in the boundary we study the transition of the mutual information given by the holographic prescription. In the case of the charged black hole, when the width of the strips becomes large this transition provides a characteristic finite distance depending on the temperature.

Electron stars for holographic metallic criticality

We refer to the ground state of a gravitating, charged ideal fluid of fermions held at a finite chemical potential as an ``electron star.'' In a holographic setting, electron stars are candidate gravity duals for strongly interacting finite fermion density systems. We show how electron stars develop an emergent Lifshitz scaling at low energies. This IR scaling region is a consequence of the two-way interaction between emergent quantum critical bosonic modes and the finite density of fermions. By integrating from the IR region to an asymptotically $Ad{S}_{4}$ spacetime, we compute basic properties of the electron stars, including their electrical conductivity. We emphasize the challenge of connecting UV and IR physics in strongly interacting finite density systems.

Lifshitz solutions of D=10 and D=11 supergravity

We construct infinite families of Lifshitz solutions of D = 10 and D = 11 supergravity with dynamical exponent z = 2. The new solutions are based on five-and seven-dimensional Einstein manifolds and are dual to field theories with Lifshitz scaling in 1+2 and 1+1 spacetime dimensions, respectively. When the Einstein spaces are Sasaki-Einstein, the solutions are supersymmetric.

Null energy condition and causality in Lifshitz holography

We use a WKB approximation to establish a relation between the wave front velocity in a strongly coupled theory and the local speed of light in a holographic dual, with our main focus put on systems with Lifshitz scaling with dynamical exponent z. We then use Einstein equations to relate the behavior of the local speed of light in the bulk with the null energy condition (NEC) for bulk matter, and we show that it is violated for Lifshitz backgrounds with z < 1. We study signal propagation in the gravity dual and show that violations of the NEC are incompatible with causality in the strongly coupled theory, ruling out as holographic models Lifshitz backgrounds with z < 1. We argue that causality violations in z < 1 theories will show up in correlators as superluminal modes and confirm this for a particular example with z = 1/2. Finally, as an application, we use z < 1 solutions to uncover regions of the parameter space of curvature squared corrections to gravity where the NEC can be violated.

Lifshitz spacetimes from AdS null and cosmological solutions

We describe solutions of 10-dimensional supergravity comprising null deformations of $AdS_5\times S^5$ with a scalar field, which have $z=2$ Lifshitz symmetries. The bulk Lifshitz geometry in 3+1-dimensions arises by dimensional reduction of these solutions. The dual field theory in this case is a deformation of the N=4 super Yang-Mills theory. We discuss the holographic 2-point function of operators dual to bulk scalars. We further describe time-dependent (cosmological) solutions which have anisotropic Lifshitz scaling symmetries. We also discuss deformations of $AdS\times X$ in 11-dimensional supergravity, which are somewhat similar to the solutions above. In some cases here, we expect the field theory duals to be deformations of the Chern-Simons theories on M2-branes stacked at singularities.

Phase transitions between Reissner-Nordstrom and dilatonic black holes in 4D AdS spacetime

We study Einstein-Maxwell-dilaton gravity models in four-dimensional antide Sitter (AdS) spacetime which admit the Reissner-Nordstrom (RN) black hole solution. We show that below a critical temperature the AdS-RN solution becomes unstable against scalar perturbations and the gravitational system undergoes a phase transition. We show using numerical calculations that the new phase is a charged dilatonic black hole. Using the AdS/CFT correspondence we discuss the phase transition in the dual field theory both for non-vanishing temperatures and in the extremal limit. The extremal solution has a Lifshitz scaling symmetry. We discuss the optical conductivity in the new dual phase and find interesting behavior at low frequencies where it shows a “Drude peak”. The resistivity varies with temperature in a non-monotonic way and displays a minimum at low temperatures which is reminiscent of the celebrated Kondo effect.

Holographic superconductors with Lifshitz scaling

Black holes in asymptotically Lifshitz spacetime provide a window onto finite temperature effects in strongly coupled Lifshitz models. We add a Maxwell gauge field and charged matter to a recently proposed gravity dual of (2+1)-dimensional Lifshitz theory. This gives rise to charged black holes with scalar hair, which correspond to the superconducting phase of holographic superconductors with z > 1 Lifshitz scaling. Along the way we analyze the global geometry of static, asymptotically Lifshitz black holes at the arbitrary critical exponent z > 1. In all known exact solutions there is a null curvature singularity in the black hole region, and, by a general argument, the same applies to generic Lifshitz black holes.

Statistics of simple chains in a sea of blockers

We carry out a simulation of freely jointed ring polymers in the presence of uncorrelated blockers on a cubic three-dimensional lattice. The size of the polymer is shown to obey Lifshitz scaling at large polymer mass. The simulation results are compared with the predictions of the RISM polaron theory [D. Chandler, Y. Singh, and D. M. Richardson, J. Chem. Phys. 81, 1975 (1984)] derived for the nearly isomorphic problem of thermal excess electrons in simple fluids. Implications of the Gaussian density field treatment of the fluid in that theory are discussed. Further comparisons are drawn between the blocker model and the quantum percolation problem. This correspondence allows us to compare the values of mobility edge (the energy of electronic states at the bottom of the conduction band) in hard-sphere-like fluids with those in lattice models.