Koji Hashimoto, Norihiro Iizuka
We present a way to include impurities in AdS/CFT correspondence, in view of its application to condensed matter physics. Examples of these are the current impurity and spin impurity. We calculate electric conductivity and spin susceptibility of holographic superconductors, with doping of density/spin impurities.
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The holographic principle in the pp-wave limit proposed in our previous works is further confirmed by studying impurity non-preserving processes which contain a fermionic BMN operator with one scalar and one fermion impurities. We show that the previously proposed duality relation between the matrix elements of the three point interaction Hamiltonian in the holographic string field theory and the OPE coefficients in super Yang-Mills theory holds to the leading order in the large $μ$ limit. Operator mixing is required to obtain the BMN operator of definite conformal dimension which corresponds …
We obtain explicit expressions for the thermoelectric transport coefficients of a strongly coupled, planar medium in the presence of an orthogonal magnetic field and momentum-dissipating processes. The computations are performed within the gauge/gravity framework where the momentum dissipation mechanism is introduced by including a mass term for the bulk graviton. Relying on the structure of the computed transport coefficients and promoting the parameters to become dynamical functions, we propose a holography inspired phenomenology open to a direct comparison with experimental data from the cu…
In this work, we examine how charge is transported in a theory where momentum is relaxed by spatially dependent, massless scalars. We analyze the possible IR phases in terms of various scaling exponents and the (ir)relevance of operators in the IR effective holographic theory with a dilaton. We compute the (finite) resistivity and encounter broad families of (in)coherent metals and insulators, characterized by universal scaling behaviour. The optical conductivity at zero temperature and low frequencies exhibits power tails which can violate scaling symmetries, due to the running of the dilaton…
Recent discovery of transport anomaly in graphene demonstrated that a system known to be weakly interacting may become strongly correlated if system parameter(s) can be tuned such that fermi surface is sufficiently small. We study the strong correlation effects in the transport coefficients of Dirac materials doped with magnetic impurity under the magnetic field using holographic method. The experimental data of magneto-conductivity are well fit by our theory, however, not much data are available for other transports of Dirac material in such regime. Therefore, our results on heat transport,th…
Transport in strongly-disordered, metallic systems is governed by diffusive processes. Based on quantum mechanics, it has been conjectured that these diffusivities obey a lower bound $D/v^2\gtrsim \hbar/k_B T$, the saturation of which provides a mechanism for the T-linear resistivity of bad metals. This bound features a characteristic velocity $v$, which was later argued to be the butterfly velocity $v_B$, based on holographic models of transport. This establishes a link between incoherent metallic transport, quantum chaos and Planckian timescales. Here we study higher derivative corrections t…
We study the magnetic effect in strongly interacting system with two conserved currents near the quantum critical point (QCP). For this purpose, we introduce the hyper-scaling violation geometry with the blackhole. Considering the perturbation near the background geometry, we compute the transport coefficients using holographic methods. We calculated the magneto-transport for general QCP and discuss the special point $(z,θ)=(3/2,1)$ where the data of Dirac material were well-described previously.
We compute the thermodynamic properties of the Sachdev-Ye-Kitaev (SYK) models of fermions with a conserved fermion number, $\mathcal{Q}$. We extend a previously proposed Schwarzian effective action to include a phase field, and this describes the low temperature energy and $\mathcal{Q}$ fluctuations. We obtain higher-dimensional generalizations of the SYK models which display disordered metallic states without quasiparticle excitations, and we deduce their thermoelectric transport coefficients. We also examine the corresponding properties of Einstein-Maxwell-scalar theories on black brane geom…
As a continuation of our previous works studying the holographic principle in the plane-wave limit, we discuss the 3-point correlation functions of BMN operators with bosonic excitations when impurities are not conserved. We show that our proposal for a holographic mapping between the conformal OPE coefficients of super Yang-Mills theory and the 3-point vertex of the holographic string field theory is valid to the leading order in the large $μ$ limit. Our results provide for the first time a direct holographic relation for the 3-point correlators of BMN operators including impurity non-preserv…
Recent experiments have uncovered evidence of the strongly coupled nature of the graphene: the Wiedemann-Franz law is violated by up to a factor of 20 near the charge neutral point. We describe this strongly-coupled plasma by a holographic model in which there are two distinct conserved U(1) currents. We find that our analytic results for the transport coefficients for two current model have a significantly improved match to the density dependence of the experimental data than the models with only one current. The additive structure in the transports coefficients plays an important role. We al…
We consider a holographic model of strongly interacting plasma with a gravitational anomaly. In this model, we compute parity-odd responses of the system at finite temperature and chemical potential to external electromagnetic and gravitational fields. Working within the linearized fluid/gravity duality, we performed the calculation up to the third order in gradient expansion. Besides reproducing the chiral magnetic(CME) and vortical (CVE) effects we also obtain gradient corrections to the CME and CVE due to the gravitational anomaly. Additionally, we find energy-momentum and current responses…
Anomalous Transport and Explicit Symmetry Breaking in Holography
本文研究了五维共形场论中纯规范和混合规范-引力Chern-Simons项对反常传输的影响，发现显式对称破缺可扩展至非反常部分，运输系数依赖于对称破缺质量参数。
In this paper we consider the energy and momentum transport in (1+1)-dimension conformal field theories (CFTs) that are deformed by an irrelevant operator $T\bar{T}$, using the integrability based generalized hydrodynamics, and holography. The two complementary methods allow us to study the energy and momentum transport after the in-homogeneous quench, derive the exact non-equilibrium steady states (NESS) and calculate the Drude weights and the diffusion constants. Our analysis reveals that all of these quantities satisfy universal formulae regardless of the underlying CFT, thereby generalizin…
We show that there are universal high-temperature relations for transport coefficients of plasmas described by a wide class of field theories with gravity duals. These theories can be viewed as strongly coupled large-Nc conformal field theories deformed by one or more relevant operators. The transport coefficients we study are the speed of sound and bulk viscosity, as well as the conductivity, diffusion coefficient, and charge susceptibility of probe U(1) charges. We show that the sound bound v_s^2 <= 1/3 is satisfied at high temperatures in these theories and also discuss bounds on the diffus…
Anomaly-induced transport phenomena in presence of strong external electromagnetic fields are explored within a 4D field theory defined holographically as $U(1)_V\times U(1)_A$ Maxwell-Chern-Simons theory in Schwarzschild-$AdS_5$. Two complementary studies are reported. In the first one, we present results on the Ohmic conductivity, diffusion constant, chiral magnetic conductivity, and additional anomaly-induced transport coefficients as functions of external e/m fields. Next, gradient resummation in a constant background magnetic field is performed. All-order resummed constitutive relations a…
We construct a 3+1 dimensional holographic model dual to a parity violating hydrodynamic system in 2+1 dimensions. Our model contains gravitational and electrodynamic Chern-Simons terms coupled to a neutral pseudo scalar $θ$, and a potential composed of quadratic and quartic terms in $θ$. The background is a charged black brane. We study the hydrodynamics to first order in spacetime derivatives near the probe limit of the pseudo scalar, by extracting the transport coefficients from the scalar, vector, and tensor modes of bulk perturbations. We study two mechanisms for breaking the parity of th…
In heavy-ion collisions, the quark-gluon plasma is produced far from equilibrium. This regime is currently inaccessible by quantum chromodynamics (QCD) computations. We calculate shear transport and entropy far from equilibrium in a holographic model, defining a time-dependent ratio of shear viscosity to entropy density, $η/s$. Large deviations of up to 60% from its near-equilibrium value, $1/4π$, are found for realistic situations at the Large Hadron Collider. We predict the far-from-equilibrium time-dependence of $η/s$ to substantially affect the evolution of the QCD plasma and to impact the…
In the presence of dense matter quantum anomalies give rise to two new transport phenomena. An anomalous current is generated either by an external magnetic field or through vortices in the fluid carrying the anomalous charge. The associated transport coefficients are the anomalous magnetic and vortical conductivities. Whereas a Kubo formula for the anomalous magnetic conductivity is well known we develop a new Kubo type formula that allows the calculation of the vortical conductivity through a two point function of the anomalous current and the momentum density. We also point out that the ano…
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…
Nonlinear transport phenomena induced by the chiral anomaly are explored within a 4D field theory defined holographically as $U(1)_V\times U(1)_A$ Maxwell-Chern-Simons theory in Schwarzschild-$AdS_5$. First, in presence of external electromagnetic fields, a general form of vector and axial currents is derived. Then, within the gradient expansion up to third order, we analytically compute all (over 50) transport coefficients. A wealth of higher order (nonlinear) transport phenomena induced by chiral anomaly are found beyond the Chiral Magnetic and Chiral Separation Effects. Some of the higher o…
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 Landau Fermi liquids, screened impurities support quasi-bound states, representing electrons bound to the impurity but making virtual excursions away. Signals of these quasi-bound states are electron-impurity scattering phase shifts and the corresponding resonances in cross sections. We consider large-$N$, strongly-coupled $(3+1)$-dimensional $\mathcal{N}=4$ supersymmetric $SU(N)$ Yang-Mills theory on the Coulomb branch, where an adjoint scalar has a non-zero expectation value that breaks $SU(N) \to SU(N-1) \times U(1)$. In the holographic dual we re-visit well-known solutions for a probe D…
Nonlinear transport phenomena induced by chiral anomaly are explored within a 4D field theory defined holographically as $U(1)_V\times U(1)_A$ Maxwell-Chern-Simons theory in Schwarzschild-$AdS_5$. In presence of weak constant background electromagnetic fields, the constitutive relations for vector and axial currents, resummed to all orders in the gradients of charge densities, are encoded in nine momenta-dependent transport coefficient functions (TCFs). These TCFs are first calculated analytically up to third order in gradient expansion, and then evaluated numerically beyond the hydrodynamic l…
We calculate the transport of a theory with two conserved currents by holographic method and compare it with graphene data to determine its dynamical exponents $(z,θ)$ which characterizes a QCP. As a result, we find that the electric and the thermal conductivity data can be fit much more naturally if we assume $(z,θ)=(3/2,1)$ rather than $(1,0)$. Furthermore, we find that thermoelectric power data at high temperature can be fit if we use $(3/2,1)$ but not at all by $(1,0)$. The $θ=1$ result can be interpreted as taking into account the fermionic nature of the electrons and $z=3/2$ can be inter…
Anomaly induced transport from symmetry breaking in holography
该研究探讨了在显式对称破缺下，反常诱导传输现象对非反常部分的影响，揭示了纯规范和混合规范-引力反常在强耦合系统中的作用。
We revisit the transport properties induced by the chiral anomaly in a charged plasma holographically dual to anomalous $U(1)_V\times U(1)_A$ Maxwell theory in Schwarzschild-$AdS_5$. Off-shell constitutive relations for vector and axial currents are derived using various approximations generalising most of known in the literature anomaly-induced phenomena and revealing some new ones. In a weak external field approximation, the constitutive relations have all-order derivatives resummed into six momenta-dependent transport coefficient functions: the diffusion, the electric/magnetic conductivity,…
Planar black holes in AdS, which are holographically dual to compressible relativistic fluids, have a long-lived phonon mode that captures the physics of attenuated sound propagation and transports energy in the plasma. We describe the open effective field theory of this fluctuating phonon degree of freedom. The dynamics of the phonon is encoded in a single scalar field whose gravitational coupling has non-trivial spatial momentum dependence. This description fits neatly into the paradigm of classifying gravitational modes by their Markovianity index, depending on whether they are long-lived. …
In this paper we obtain holographic formulas for the transport coefficients $κ$ and $τ_π$ present in the second-order derivative expansion of relativistic hydrodynamics in curved spacetime associated with a non-conformal strongly coupled plasma described holographically by an Einstein+Scalar action in the bulk. We compute these coefficients as functions of the temperature in a bottom-up non-conformal model that is tuned to reproduce lattice QCD thermodynamics at zero baryon chemical potential. We directly compute, besides the speed of sound, 6 other transport coefficients that appear at second…
We discuss a possible dependence of the chiral magnetic effect (CME) on the elliptic flow coefficient v2. We first study this in a hydrodynamic model for a static anisotropic plasma with multiple anomalous U(1) currents. In the case of two charges, one axial and one vector, the CME formally appears as a first-order transport coefficient in the vector current. We compute this transport coefficient and show its dependence on v2. We also determine the CME-coefficient from first-order corrections to the dual AdS background using the fluid-gravity duality. For small anisotropies, we find numerical …
We use the AdS/CFT correspondence to study first-order relativistic viscous magneto-hydrodynamics of (2+1) dimensional conformal magnetic fluids. It is shown that the first order magneto-hydrodynamics constructed following Landau and Lifshitz from the positivity of the entropy production is inconsistent. We propose additional contributions to the entropy motivated dissipative current and, correspondingly, new dissipative transport coefficients. We use the strongly coupled M2-brane plasma in external magnetic field to show that the new magneto-hydrodynamics leads to self-consistent results in t…
Holography and Optimal Transport: Emergent Wasserstein Spacetime in Harmonic Oscillator, SYK and Krylov Complexity
本文探讨了全息时空如何通过最优传输从量子系统中涌现，以谐振子、SYK模型和Krylov复杂性为例，展示Wasserstein空间的形成及其与黑洞几何的一致性。
An effective description of charge diffusion and energy transport in a charged plasma from holography
本文通过将带电等离子体全息建模为Reissner-Nordstrom-AdS黑洞，解耦纵向涨落并分离声子模与电荷扩散模，构建了包含推迟响应和随机涨落、精确到梯度四阶的实时高斯有效作用量。
We obtain the thermal photon and dilepton production rates in a strongly coupled quark-gluon plasma (QGP) at both zero and nonzero baryon chemical potential using a bottom-up Einstein-Maxwell-Dilaton (EMD) holographic model that is in good quantitative agreement with the thermodynamics of $(2+1)$-flavor lattice QCD around the crossover transition for baryon chemical potentials up to 400 MeV, which may be reached in the beam energy scan (BES) at RHIC. We find that increasing the temperature $T$ and the baryon chemical potential $μ_B$ enhances the peak present in both spectra. We also obtain the…
Momentum relaxation is an ever-present and unavoidable ingredient of any realistic condensed matter system. In real-world materials the presence of a lattice, impurities or disorder forces momentum to dissipate and leads to relevant physical effects such as the finiteness of the DC transport properties, i.e. conductivities. The main purpose of this thesis is the introduction of momentum dissipation and its consequent effects into the framework of AdS/CMT, namely the applications of the gauge-gravity duality to condensed matter. A convenient and effective way of breaking the translational symme…
This is a second study of chiral anomaly induced transport within a holographic model consisting of anomalous $U(1)_V\times U(1)_A$ Maxwell theory in Schwarzschild-$AdS_5$ spacetime. In the first part, chiral magnetic/separation effects (CME/CSE) are considered in presence of a static spatially-inhomogeneous external magnetic field. Gradient corrections to CME/CSE are analytically evaluated up to third order in the derivative expansion. Some of the third order gradient corrections lead to an anomaly-induced negative $B^2$-correction to the diffusion constant. We also find non-linear in $B$ mod…
A relativistic fluid in 3+1 dimensions with a global $U(1)$ symmetry admits nine independent static susceptibilities at the second order in the hydrodynamic derivative expansion, which capture the response of the fluid in thermal equilibrium to the presence of external time-independent sources. Of these, seven are time-reversal $\mathbb{T}$ invariant and can be obtained from Kubo formulas involving equilibrium two-point functions of the energy-momentum tensor and the $U(1)$ current. Making use of the gauge/gravity duality along with the aforementioned Kubo formulas, we compute all seven $\math…
Estimate for the bulk viscosity of strongly coupled quark matter using perturbative QCD and holography
本文结合微扰QCD与全息方法，推导出未配对夸克物质体粘滞系数的改进弱耦合与新强耦合结果，并整合为一个适用于天体物理条件的解析口袋公式。
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