Holographic heavy quark potential, free energy, and running coupling in backgrounds with broken translational symmetry: Separating finite density from momentum relaxation
School of Mathematics and Physics, China University of Geosciences（中国地质大学数学与物理学院）
We study heavy quark observables, namely the static interquark potential, the thermal free energy, and the running coupling, in a five dimensional asymptotically anti-de Sitter (AdS) spacetime with broken translational symmetry. The Einstein-Maxwell-axion (EMa) geometry contains two independent scales: the chemical potential $μ$, which controls finite baryon density, and the translational symmetry breaking parameter $β$, which controls momentum relaxation. Using high precision numerical calculations at finite temperature and at zero temperature, we show that both scales weaken color interactions and promote quarkonium dissociation in a strongly coupled quark gluon plasma, although the underlying mechanisms differ. The chemical potential dominates color screening and strongly modifies the heavy quark potential and running coupling, whereas $β$ mainly changes the plasma entropy and therefore gives the leading correction to the thermal free energy. At zero temperature, thermal contributions vanish and the renormalized free energy reduces to a static potential modified by the medium, with an approximately Coulombic form. At all temperatures, a finite baryon density suppresses the binding of quark antiquark ($Q\bar{Q}$) pairs much more strongly than momentum relaxation. We extract the color screening length and dissociation scale, and discuss implications for quarkonium production in heavy ion collisions. These results show that static color interactions and thermodynamic observables are controlled by different medium scales, which offers a unified picture of heavy quark probes in dense dissipative plasmas.
We comment on a simple way to accommodate translational symmetry breaking into the recently proposed holographic model which features a superconducting dome-shaped region on the temperature-doping phase diagram.
The density response of charged liquids contains a collective excitation known as the plasmon. In holographic systems with translational invariance the origin of this collective excitation is traced back to the presence of zero-sound. Using a holographic model in which translational symmetry is broken pseudo-spontaneously, we show the density response is not dominated by a single isolated mode at low momentum and temperature. As a consequence, the density response contains a broad asymmetric peak with an attenuation which does not increase monotonically with momentum and temperature.
We revisit HHH model in [Phys. Rev. Lett. {\bf 101}, 031601 (2008)] and extend the ansatz of matter fields to being of depending on a spatial dimension except the holographic direction. Despite homogeneous solutions of ground and excited states, especially for the excited states, there also exists solutions where the translational invariance is broken. It is worth mentioning that no periodic sources are assigned to the matter fields, so the translational symmetry is broken spontaneously. We investigate how the new solutions and the condensates of excited states develop with the change of tempe…
We consider holographic superconductors in a broad class of massive gravity backgrounds. These theories provide a holographic description of a superconductor with broken translational symmetry. Such models exhibit a rich phase structure: depending on the values of the temperature and the disorder strength the boundary system can be in superconducting, normal metallic or normal pseudoinsulating phases. Furthermore the system supports interesting collective excitation of the charge carriers, which appears in the normal phase, persists in the superconducting phase, but eventually gets destroyed b…
It is presently unknown how strong lattice potentials influence the fermion spectral function of the holographic strange metals predicted by the AdS/CFT correspondence. This embodies a crucial test for the application of holography to condensed matter experiments. We show that for one particular momentum direction this spectrum can be computed for arbitrary strength of the effective translational symmetry breaking potential of the so-called Bianchi-VII geometry employing ordinary differential equations. Deep in the strange metal regime we find rather small changes to the single-fermion respons…
In this paper we investigate the ratio of shear viscosity to entropy density, $η/s$, in hyperscaling violating geometry with lattice structure. We show that the scaling relation with hyperscaling violation gives a strong constraint to the mass of graviton and usually leads to a power law of temperature, $η/s\sim T^κ$. We find the exponent $κ$ can be greater than two such that the new bound for viscosity raised in arXiv:1601.02757 is violated. Our above observation is testified by constructing specific solutions with UV completion in various holographic models. Finally, we compare the boundedne…
We study the shear viscosity in an effective hydrodynamic theory and holographic model where the translational symmetry is broken by massless scalar fields. We identify the shear viscosity, $η$, from the coefficient of the shear tensor in the modified constitutive relation, constructed from thermodynamic quantities, fluid velocity and the scalar fields, which break the translational symmetry explicitly. Our construction of constitutive relation is inspired by those derived from the fluid/gravity correspondence in the weakly disordered limit $m/T \ll 1$. We show that the shear viscosity from th…
In a holographic probe-brane model exhibiting a spontaneously spatially modulated ground state, we introduce explicit sources of symmetry breaking in the form of ionic and antiferromagnetic lattices. For the first time in a holographic model, we demonstrate pinning, in which the translational Goldstone mode is lifted by the introduction of explicit sources of translational symmetry breaking. The numerically computed optical conductivity fits very well to a Drude-Lorentz model with a small residual metallicity, precisely matching analytic formulas for the DC conductivity. We also find an instab…
We provide a complete and unified description of translational symmetry breaking in a simple holographic model. In particular, we focus on the distinction and the interplay between explicit and spontaneous breaking. We consider a class of holographic massive gravity models which allow to range continuously from one situation to the other. We study the collective degrees of freedom, the electric AC conductivity and the shear correlator in function of the explicit and spontaneous scales. We show the possibility of having a sound-to-diffusion crossover for the transverse phonons. Within our model…
We present a class of holographic massive gravity models that realize a spontaneous breaking of translational symmetry - they exhibit transverse phonon modes whose speed relates to the elastic shear modulus according to elasticity theory. Massive gravity theories thus emerge as versatile and convenient theories to model generic types of translational symmetry breaking: explicit, spontaneous and a mixture of both. The nature of the breaking is encoded in the radial dependence of the graviton mass. As an application of the model, we compute the temperature dependence of the shear modulus and fin…
In this note we study the effects of a magnetic field on transport using holographic models with broken translational invariance. We show that, after carefully subtracting off non-trivial magnetisation currents, it is possible to express the DC transport currents of the boundary theory in terms of properties of a black hole horizon. This allows us to obtain simple analytic expressions for the electrical, thermoelectric and heat conductivity tensors. Our results apply to both isotropic and anisotropic models, including holographic Q-lattices and to certain theories where translational invarianc…
It has been shown that holographic massive gravities can effectively realize the states with spontaneous breaking of translational symmetry in a homogenous manner. In this work, we consider a toy model of such category by adding a special gauge-axion coupling to the bulk action. Firstly, we identify the existence of spontaneous breaking of translations by the UV analysis. In the absence of explicit breaking, the black hole solution is simply the same as the Reissner-Nodstrom(RN) black holes, regardless of the non-trivial profile of the bulk axions. The associated Goldstone modes exist only whe…
We discuss new types of instabilities of D=4 electrically charged AdS-Reissner-Nordström black branes that involve neutral pseudo-scalars. The instabilities spontaneously break translational invariance and are associated with the dual three-dimensional CFTs, at finite temperature and fixed chemical potential with respect to a global abelian symmetry, acquiring striped phases. We show that such instabilities are present for the infinite class of skew-whiffed $AdS_4\times SE_7$ solutions of D=11 supergravity, albeit at a lower temperature than the known superfluid instabilities.
We investigate holographic fermions in uni-directional striped phases, where the breaking of translational invariance can be generated either spontaneously or explicitly. We solve the Dirac equation for a probe fermion in the associated background geometry. When the spatial modulation effect becomes sufficiently strong, we see a spectral weight suppression whenever the Fermi surface is larger than the first Brillouin zone. This leads to the gradual disappearance of the Fermi surface along the symmetry breaking direction, in all of the cases we have examined. This effect appears to be a generic…
We consider the effects of momentum relaxation on the topological quantum phase transitions in holographic Weyl semimetals. The translational symmetry breaking in the field theory is realized in the framework of massive gravity. We find that the critical value of the phase transition, characterized by the anomalous Hall conductivity, decreases with the increasing of graviton mass, i.e. the momentum relaxation strength. There exists a critical value of graviton mass above which the topological phase transition disappears and therefore the Weyl points are destroyed. All these phenomena are quali…
In this paper, we show that a simple generalization of the holographic axion model can realize spontaneous breaking of translational symmetry by considering a special gauge-axion higher derivative term. The finite real part and imaginary part of the stress tensor imply that the dual boundary system is a viscoelastic solid. By calculating quasi-normal modes and making a comparison with predictions from the elasticity theory, we verify the existence of phonons and pseudo-phonons, where the latter is realized by introducing a weak explicit breaking of translational symmetry, in the transverse cha…
Holographic low-energy spectral weight at zero temperature and finite momenta indicates the presence of a strongly coupled remnant of Pauli exclusion. Building upon previous work, we study the spectral weight of a bottom-up holographic superfluid model with spontaneously broken translational symmetry. We determine the effect of this symmetry breaking on the previously known attributes of the holographic superconductor spectral weight: 1) an instability at finite momenta and 2) the presence of nested Fermi surfaces (sometimes called Fermi shells). We find that the symmetry breaking seems to str…
The DC thermoelectric conductivities of holographic systems in which translational symmetry is broken can be efficiently computed in terms of the near-horizon data of the dual black hole. By calculating the frequency dependent conductivities to the first subleading order in the momentum relaxation rate, we give a physical explanation for these conductivities in the simplest such example, in the limit of slow momentum relaxation. Specifically, we decompose each conductivity into the sum of a coherent contribution due to momentum relaxation and an incoherent contribution, due to intrinsic curren…
Bianchi black branes (black brane solutions with homogeneous but anisotropic horizons classified by the Bianchi type) provide a simple holographic setting with lattice structures taken into account. In the case of holographic superconductor, we have a persistent current with lattices. Accordingly, we expect that in the dual gravity side, a black brane should carry some momentum along a direction of lattice structure, where translational invariance is broken. Motivated by this expectation, we consider whether---and if possible, in what circumstances---a Bianchi black brane can have momentum alo…
We discuss the DC conductivity of holographic theories with translational invariance broken by a background lattice. We show that the presence of the lattice induces an effective mass for the graviton via a gravitational version of the Higgs mechanism. This allows us to obtain, at leading order in the lattice strength, an analytic expression for the DC conductivity in terms of the size of the lattice at the horizon. In locally critical theories this leads to a power law resistivity that is in agreement with an earlier field theory analysis of Hartnoll and Hofman.
We study a holographic gauge theory dual to the D3/D5 intersection. We consider a pure gauge B-field flux through the internal two-sphere wrapped by the probe D5--brane, which corresponds to a non-commutative configuration of adjoint scalars. There is a domain wall separating the theory into regions with different ranks of the adjoint group. At zero temperature the theory is supersymmetric and at finite temperature there is a critical point of a second order phase transition. We study the corresponding critical exponents and find that the second derivatives of the free energy, with respect to …
When the system with internal tendency to a spontaneous formation of a spatially periodic state is brought in contact with the external explicit periodic potential, the interesting phenomenon of commensurate lock in can be observed. In case when the explicit potential is strong enough and its period is close to the period of the spontaneous structure, the latter is forced to assume the periodicity of the former and the commensurate state becomes a thermodynamically preferred one. If instead the two periods are significantly different, the incommensurate state is formed. It is characterized by …
Suggested holographic duals of QCD, based on AdS/CFT duality, predict that one should be able to vary the scales of colour confinement and chiral-symmetry breaking independently. Furthermore they suggest that such independent variation of scales can be achieved by the inclusion of extra 4-fermion interactions in QCD. We simulate lattice QCD with such extra 4-fermion terms at finite temperatures and show that for strong enough 4-fermion couplings the deconfinement transition occurs at a lower temperature than the chiral-symmetry restoration transition. Moreover the separation of these transitio…
Recently holographic techniques have been used to study the thermal properties of N=2 super-Yang-Mills theory, with gauge group SU(Nc) and coupled to Nf << Nc flavours of fundamental matter, at large Nc and large 't Hooft coupling. Here we consider the phase diagram as a function of temperature and baryon chemical potential mu. For fixed mu < Nc Mq there is a line of first order thermal phase transitions separating a region with vanishing baryon density and one with nonzero density. For fixed mu > Nc Mq there is no phase transition as a function of the temperature and the baryon density is alw…
We discuss the possible phases dual to the AdS hairy black holes in Horndeski theory. In the probe limit breaking the translational invariance, we study the conductivity and we find a non-trivial structure indicating a collective excitation of the charge carriers as a competing effect of momentum dissipation and the coupling of the scalar field to Einstein tensor. Going beyond the probe limit, we investigate the spontaneous breaking of translational invariance near the critical temperature and discuss the stability of the theory. We consider the backreaction of the charged scalar field to the …
We examine a holographic model in which a U(1) symmetry and translational invariance are broken spontaneously at the same time. Our construction provides an example of a system with pair-density wave order, in which the superconducting order parameter is spatially modulated but has a zero average. In addition, the charge density oscillates at twice the frequency of the scalar condensate. Depending on the choice of parameters, the model also admits a state with co-existing superconducting and charge density wave orders, in which the scalar condensate has a uniform component.
We propose massive gravity as a holographic framework for describing a class of strongly interacting quantum field theories with broken translational symmetry. Bulk gravitons are assumed to have a Lorentz-breaking mass term as a substitute for spatial inhomogeneities. This breaks momentum-conservation in the boundary field theory. At finite chemical potential, the gravity duals are charged black holes in asymptotically anti-de Sitter spacetime. The conductivity in these systems generally exhibits a Drude peak that approaches a delta function in the massless gravity limit. Furthermore, the opti…
We show that holographic models of QCD predict the presence of a Chern-Simons coupling between vector and axial-vector mesons at finite baryon density. In the AdS/CFT dictionary, the coefficient of this coupling is proportional to the baryon number density, and is fixed uniquely in the five-dimensional holographic dual by anomalies in the flavor currents. For the lightest mesons, the coupling mixes transverse $ρ$ and $a_1$ polarization states. At sufficiently large baryon number densities, it produces an instability, which causes the $ρ$ and $a_1$ mesons to condense in a state breaking both ro…
As evidence for the ER=EPR conjecture, it has recently been observed that the string that is holographically dual to an entangled quark-antiquark pair separating with (asymptotically) uniform acceleration has a wormhole on its worldsheet. We point out that a two-sided horizon and a wormhole actually appear for much more generic quark-antiquark trajectories, which is consistent with the fact that the members of an EPR pair need not be permanently out of causal contact. The feature that determines whether the causal structure of the string worldsheet is trivial or not turns out to be the emissio…
We study the elastic response of planar black hole (BH) solutions in a simple class of holographic models with broken translational invariance. We compute the transverse quasi-normal mode spectrum and the propagation speed of the lowest energy mode. We find that the speed of the lowest mode relates to the BH rigidity modulus as dictated by elasticity theory. This allows to identify these modes as transverse phonons---the pseudo Goldstone bosons of spontaneously broken translational invariance. In addition, we show that these modes have a mass gap controlled by an explicit source of the transla…
We study the holographic Schwinger effect with magnetic field at RHIC and LHC energies by using the AdS/CFT correspondence. We consider both weak and strong magnetic field cases with $B\ll T^2$ and $B\gg T^2$ solutions respectively. Firstly, we calculate separating length of the particle pairs at finite magnetic field. It is found that for both weak and strong magnetic field solutions the maximum value of separating length decreases with the increase of magnetic field , which can be inferred that the virtual electron-positron pairs become real particles more easily. We also find that the magne…
We analyze the concomitant spontaneous breaking of translation and conformal symmetries by introducing in a CFT a complex scalar operator that acquires a spatially dependent expectation value. The model, inspired by the holographic Q-lattice, provides a privileged setup to study the emergence of phonons from a spontaneous translational symmetry breaking in a conformal field theory and offers valuable hints for the treatment of phonons in QFT at large. We first analyze the Ward identity structure by means of standard QFT techniques, considering both spontaneous and explicit symmetry breaking. N…
Holographic properties of a finite density fermion system have been shown to exhibit many interesting behaviours which can be observed in future. In this paper, we study low energy fermion properties in the framework of the holographic Mott-Insulator system. We study the nature of the Fermi surface and its evolution by tuning two types of dipole couplings in the bulk. We further introduce translational symmetry breaking complex scalar field, which is assumed to couple with the holographic fermions. The symmetry breaking background induced by the scalar field is known as Q-lattice. We calculate…
A supersolid is a system that presents long-range order and shear rigidity as a solid but which also supports a non-dissipative superflow as a superfluid. From an effective perspective, supersolids are identified with phases of matter that break spontaneously translational invariance together with a global $U(1)$ symmetry. By using this symmetry prescription, we build a holographic bottom-up model for supersolids and we start the investigation of its thermodynamic and mechanical properties. More precisely, we analyze the behaviour of the critical temperature, the condensate, the shear modulus …
In the holographic approach to cosmology, cosmological observables are described in terms of correlators of a three-dimensional boundary quantum field theory. As a concrete model, we study the 3$d$ massless $SU(N)$ scalar matrix field theory. In this work, we focus on the renormalisation of the energy-momentum tensor 2-point function, which can be related to the CMB power spectra. Here we present a non-perturbative procedure to remove divergences resulting from the loss of translational invariance on the lattice, by imposing Ward identities. This will allow us to make predictions for the CMB p…
We construct the holographic renormalization group (RG) flow of thermo-electric conductivities when the translational symmetry is broken. The RG flow is probed by the intrinsic observers hovering on the sliding radial membranes. We obtain the RG flow by solving a matrix-form Riccati equation. The RG flow provides a high-efficient numerical method to calculate the thermo-electric conductivities of strongly coupled systems with momentum dissipation. As an illustration, we recover the AC thermo-electric conductivities in the Einstein-Maxwell-axion model. Moreover, in several homogeneous and isotr…
We consider the spontaneous breaking of translational symmetry and identify the associated Goldstone mode -- a longitudinal phonon -- in a holographic model with Bianchi VII helical symmetry. For the first time in holography, we observe the pinning of this mode after introducing a source for explicit breaking compatible with the helical symmetry of our setup. We study the dispersion relation of the resulting pseudo-Goldstone mode, uncovering how its speed and mass gap depend on the amplitude of the source and temperature. In addition, we extract the optical conductivity as a function of freque…
The Einstein-Maxwell-Axion-Dilaton (EMAD) theories, based on the Gubser-Rocha (GR) model, are very interesting in holographic calculations of strongly correlated systems in the condensed matter physics. Due to the presence of spatially dependent massless axionic scalar fields, the momentum is relaxed and we have no translational invariance at finite charge density. It would be of interest to study some aspects of quantum information theory for such systems in the context of $AdS/CFT$ where EMAD theory is a holographic dual theory. For instance, in this paper we investigate the complexity and i…
A black hole described in $SU(N)$ gauge theory consists of $N$ D-branes. By separating one of the D-branes from others and studying the interaction between them, the black hole geometry can be probed. In order to obtain quantitative results, we employ the lattice Monte Carlo simulation. As a proof of the concept, we perform an explicit calculation in the matrix model dual to the black zero-brane in type IIA string theory. We demonstrate this method actually works in the high temperature region, where the stringy correction is large. We argue possible dual gravity interpretations.
We construct a gravity dual for charge density waves (CDW) in which the translational symmetry along one spatial direction is spontaneously broken. Our linear perturbation calculation on the gravity side produces the frequency dependence of the optical conductivity, which exhibits the two familiar features of charge density waves, namely the pinned collective mode and gapped single-particle excitation. These two features indicate that our gravity dual also provides a new mechanism to implement the metal to insulator phase transition by CDW, which is further supported by the fact that d.c. cond…
In this letter we study the Hall conductivity in holographic models where translational invariance is broken by a lattice. We show that generic holographic theories will display a different temperature dependence in the Hall angle as to the DC conductivity. Our results suggest a general mechanism for obtaining an anomalous scaling of the Hall angle in strongly interacting quantum critical systems.
We present a holographic theory in AdS_4 whose zero temperature ground state develops a crystal structure, spontaneously breaking translational symmetry. The crystal is induced by a background magnetic field, but requires no chemical potential. This lattice arises from the existence of 't Hooft-Polyakov monopole solitons in the bulk which condense to form a classical object known as a monopole wall. In the infra-red, the magnetic field is screened and there is an emergent SU(2) global symmetry.
We study the dynamics and the relaxation of bulk plasmons in strongly coupled and quantum critical systems using the holographic framework. We analyze the dispersion relation of the plasmonic modes in detail for an illustrative class of holographic bottom-up models. Comparing to a simple hydrodynamic formula, we entangle the complicated interplay between the three least damped modes and shed light on the underlying physical processes. Such as the dependence of the plasma frequency and the effective relaxation time in terms of the electromagnetic coupling, the charge and the temperature of the …
At finite charge density certain holographic models exhibit the spontaneous breaking of translational invariance resulting in an inhomogeneous phase. We follow up on recent numerical work, reporting results for a larger class of cohomogeneity two black branes in AdS, dual to a holographic striped phase. We construct the continuous moduli space of inhomogeneous black branes as a function of the temperature. Minimising the free energy we determine the dominant striped solutions, revealing a growth in the stripe size as the system is cooled. We discuss the thermodynamic properties of this line of…
Large-N_c QCD matter at intermediate baryon density and low temperatures has been conjectured to be in the so-called quarkyonic phase, i.e., to have a quark Fermi surface and on top of it a confined spectrum of excitations. It has been suggested that the presence of the quark Fermi surface leads to a homogeneous phase with restored chiral symmetry, which is unstable towards creating condensates breaking both the chiral and translational symmetry. Motivated by these exotic features, we investigate properties of cold baryonic matter in the single flavor Sakai-Sugimoto model searching for a holog…
In this work, we uncover a universal relaxation mechanism of pinned density waves, combining Gauge/Gravity duality and effective field theory techniques. Upon breaking translations spontaneously, new gapless collective modes emerge, the Nambu-Goldstone bosons of broken translations. When translations are also weakly broken (eg by disorder or lattice effects), these phonons are pinned with a mass $m$ and damped at a rate $Ω$, which we explicitly compute. This contribution to $Ω$ is distinct from that of topological defects. We show that $Ω\simeq G m^2Ξ$, where $G$ is the shear modulus and $Ξ$ i…
The relationship between thermodynamics and the Lloyd bound on the holographic complexity for a black hole has been of interest. We consider $D$ dimensional anti-de Sitter black holes with hyperbolic geometry as well as black holes with momentum relaxation that have a minimum for temperature and mass. We show that the singular points of the thermodynamic curvature of the black holes, as thermodynamic systems, correspond to the zero points of the action and volume complexity at the Lloyd bound. For such black holes with a single horizon, the complexity of volume and the complexity of action at …
We study (fermionic) spectral functions in two holographic models, the Gubser-Rocha-linear axion model and the linear axion model, where translational symmetry is broken by axion fields linear to the boundary coordinates ($ψ_{I}=βδ_{Ii} x^{i}$). Here, $β$ corresponds to the strength of momentum relaxation. The spectral function is computed by the fermionic Green's function of the bulk Dirac equation, where a fermion mass, $m$, and a dipole coupling, $p$, are introduced as input parameters. By classifying the shape of spectral functions, we construct complete phase diagrams in ($m,p,β$) space f…
We construct inhomogeneous asymptotically AdS black hole solutions corresponding to the spontaneous breaking of translational invariance and the formation of striped order in the boundary field theory. We find that the system undergoes a second order phase transition in both the fixed density and fixed chemical potential ensembles, for sufficiently large values of the axion coupling. We investigate the phase structure as function of the temperature, axion coupling and the stripe width. The bulk solutions have striking geometrical features related to a magnetoelectric effect associated with the…
We analyze the phase diagram of N=4 supersymmetric Yang-Mills theory with fundamental matter in the presence of a background magnetic field and nonzero baryon number. We identify an isolated quantum critical point separating two differently ordered finite density phases. The ingredients that give rise to this transition are generic in a holographic setup, leading us to conjecture that such critical points should be rather common. In this case, the quantum phase transition is second order with mean-field exponents. We characterize the neighborhood of the critical point at small temperatures and…
We analyze fermionic response of strongly correlated holographic matter in presence of inhomogeneous periodically modulated potential mimicking the crystal lattice. The modulation is sourced by a scalar operator that explicitly breaks the translational symmetry in one direction. We compute the fermion spectral function and show that it either exhibits a well defined Fermi surface with umklapp gaps opening on the Brillouin zone boundary at small lattice wave vector, or, when the wave vector is large, the Fermi surface is anisotropically deformed and the quasiparticles get significantly broadene…
The problem of holographic thermalization in the framework of Einstein gravity coupled to Born-Infeld nonlinear electrodynamics is investigated. We use equal time two-point correlation functions and expectation values of Wilson loop operators in the boundary quantum field theory as probes of thermalization, which have dual gravity descriptions in terms of geodesic lengths and minimal area surfaces in the bulk spacetime. The full range of values of the chemical potential per temperature ratio on the boundary is explored. The numerical results show that the effect of the charge on the thermaliza…
We examine transport in a holographic model in which the dynamics of the charged degrees of freedom is described by the nonlinear Dirac-Born-Infeld (DBI) action. Axionic scalar fields are included to break translational invariance and generate momentum dissipation in the system. Scaling exponents are introduced by using geometries which are nonrelativistic and hyperscaling-violating in the infrared. In the probe DBI limit the theory reproduces the anomalous temperature dependence of the resistivity and Hall angle of the cuprate strange metals, $ρ\sim T$ and $\cotΘ_H \sim T^2$. These scaling la…
