Quantum liquids are characterized by the distinctive properties such as the low temperature behavior of heat capacity and the spectrum of low-energy quasiparticle excitations. In particular, at low temperature, Fermi liquids exhibit the zero sound, predicted by L. D. Landau in 1957 and subsequently observed in liquid He-3. In this paper, we ask a question whether such a characteristic behavior is present in theories with holographically dual description. We consider a class of gauge theories with fundamental matter fields whose holographic dual in the appropriate limit is given in terms of the Dirac-Born-Infeld action in AdS_{p+1} space. An example of such a system is the N=4 SU(N_c) supersymmetric Yang-Mills theory with N_f massless N=2 hypermultiplets at strong coupling, finite baryon number density, and low temperature. We find that these systems exhibit a zero sound mode despite having a non-Fermi liquid type behavior of the specific heat. These properties suggest that holography identifies a new type of quantum liquids.
Using gauge/gravity duality techniques, we discuss the sound-channel retarded correlators of vector and tensor conserved currents in a class of $(2+1)$-dimensional strongly-coupled field theories at zero temperature and finite charge density, assumed to be holographically dual to the extremal Reissner-Nordström AdS$_4$ black hole. Using a combination of analytical and numerical methods, we determine the quasinormal mode spectrum at finite momentum for the coupled gravitational and electromagnetic perturbations, and discuss the appropriate choice of gauge-invariant variables (master fields) in …
We show that in a general class of strongly interacting theories at high temperatures the speed of sound approaches the conformal value c_s^2=1/3 universally from_below_. This class includes theories holographically dual to a theory of gravity coupled to a single scalar field, representing the operator of the scale anomaly.
We investigate the speed of sound in $(d+1)$-dimensional field theory by studying its dual $(d+2)$-dimensional gravity theory from gauge/gravity correspondence. Instead of the well known conformal limit $c_s^2 \rightarrow 1/d$ at high temperature, we reveal two more universal quantities in various limits: $c_s^2 \rightarrow (d-1)/16π$ at low temperature and $c_s^2 \rightarrow (d-1)/16πd$ at large chemical potential.
We show that the squared speed of sound v_{s}^{2} is bounded from above at high temperatures by the conformal value of 1/3 in a class of strongly coupled four-dimensional field theories, given some mild technical assumptions. This class consists of field theories that have gravity duals sourced by a single scalar field. There are no known examples to date of field theories with gravity duals for which v_{s}^{2} exceeds 1/3 in energetically favored configurations. We conjecture that v_{s}^{2}=1/3 represents an upper bound for a broad class of four-dimensional theories.
At zero temperature, the charge current operator appears to be conserved, within linear response, in certain holographic probe brane models of strange metals. At small but finite temperature, we analytically show that the weak non-conservation of this current leads to both a collective "zero sound" mode and a Drude peak in the electrical conductivity. This simultaneously resolves two outstanding puzzles about probe brane theories. The nonlinear dynamics of the current operator itself appears qualitatively different.
We systematically investigate the sound modes of momentum dissipated holographic systems. In particular, we focus on the Einstein-linear axions and the Einstein-Maxwell-dilaton-axion theories in four-dimensional bulk spacetime dimensions. The sound velocities of the two theories are computed respectively and the sound attenuation of the Einstein-Maxwell-axion theory is also calculated analytically. We also obtain numeral dispersion relations in the two theories which match with our analytical results. Our results show that the sound velocity of the Einstein-Maxwell-dilaton theory with addition…
We investigate the signatures of Fermi liquid formation in the N=4 super Yang-Mills theory coupled to fundamental hypermultiplet at nonvanishing chemical potential for the global U(1) vector symmetry. At strong 't Hooft coupling the system can be analyzed in terms of the D7 brane dynamics in AdS_5 x S^5 background. The phases with vanishing and finite charge density are separated at zero temperature by a quantum phase transition. In case of vanishing hypermultiplet mass, Karch, Son and Starinets discovered a gapless excitation whose speed equals the speed of sound. We find that this zero sound…
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 reve…
Hyperscaling violating `strange metal' phase of heavy fermion compounds can be described holographically by probe D-branes in the background of a Lifshitz space-time (dynamical exponent $z$ and spatial dimensions $d$) with hyperscaling violation (corresponding exponent $θ$). Without the hyperscaling violation, strange metals are known to exhibit zero sound mode for $z<2$ analogous to the Fermi liquids. In this paper, we study its fate in the presence of hyperscaling violation and find that in this case the zero sound mode exists for $z < 2(1+|θ|/d)$, where the positivity of the specific heat a…
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…
The plasmon is a ubiquitous collective mode in charged liquids. Due to the long-range Coulomb interaction, the massless zero sound mode of the neutral system acquires a finite plasmon frequency in the long-wavelength limit. In the zero-temperature state of conventional metals -- the Fermi liquid -- the plasmon lives infinitely long at long wavelength when the system is (effectively) translationally invariant. In contrast, we will show that in strongly entangled strange metals the protection of zero sound fails at finite frequency and plasmons are always short lived regardless of their waveleng…
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. …
We study quark-antiquark potential using the AdS/CFT correspondence in the BTZ black hole with non-zero angular momentum. Using explicit form of string configurations relevant to a calculation of the potential we find that the potential exhibits different dependencies on angular momentum values in the Euclidean and the Lorentzian signatures of the BTZ.
Within an extended soft wall model, we study the temperature dependence of the lowest vector meson states. Scales are adjusted by using as input the $ρ$ meson mass in vacuum and the velocity of sound from lattice QCD which displays a minimum at $T_{\rm c}$. The melting of the $ρ$ meson occurs at temperatures $\mathcal{O}(T_{\rm c})$.
We show how Higgs phases at non-zero density can be described using a simple analytic method for gauge theories possessing a holographic dual. We introduce co-dimension one branes in a bottom-up gravity dual that are sources of form flux, such that the effective curvature radius is changed when the brane is crossed. This mimics the expected flow produced by color branes nucleating in a top-down model.
In this work, we show how states with conserved numbers of dynamical defects (strings, domain walls, etc.) can be understood as possessing generalised global symmetries even when the microscopic origins of these symmetries are unknown. Using this philosophy, we build an effective theory of a $2+1$-dimensional fluid state with two perpendicular sets of immersed elastic line defects. When the number of defects is independently conserved in each set, then the state possesses two one-form symmetries. Normally, such viscoelastic states are described as fluids coupled to Goldstone bosons associated …
We show how causal relativistic Navier-Stokes equations arise from the relativistic Boltzmann equation: the causality is preserved via a judicious choice of the zero modes of the collision operator. A completely analogous procedure may be used to extract causal hydrodynamics from the fluid-gravity correspondence: again, causality of the hydrodynamic equations is preserved by a suitable choice of zero modes of the corresponding differential operators in the bulk. We give examples of zero modes which give rise to causal hydrodynamic equations for non-conformal fluids with a conserved U(1) global…
We use holographic techniques to study the zero-temperature limit of dissipation for a Brownian particle moving in a strongly coupled CFT at finite temperature in various space-time dimensions. The dissipative term in the boundary theory for $ω\to 0$, $T \to 0$ with $ω/ T$ held small and fixed, does not match the same at $T=0$, $ω\to 0$. Thus the $T\to 0$ limit is not smooth for $ω< T$. This phenomenon appears to be related to a confinement-deconfinement phase transition at $T=0$ in the field theory.
The string theory calculation of the 1/2-BPS circular Wilson loop of N=4 SYM in the planar limit at next to leading order at strong coupling is revisited in the ratio of its semiclassical string partition function and the one dual to a latitude Wilson loop with trivial expectation value. After applying a conformal transformation from the disk to the cylinder, this problem can be approached by means of the Gel'fand-Yaglom formalism. Using results from the literature and the exclusion of zero modes from a modified Gel'fand-Yaglom formula, we obtain matching with the known field theory result. As…
Within the context of AdS/CFT, the gravity dual of an s-wave superfluid is given by scalar QED on an asymptotically AdS spacetime. While this conclusion is vastly supported by numerical arguments, here we provide an analytical proof that this is indeed the case. Working at zero temperature, we explicitly find the quadratic action for the superfluid phonon at the boundary in an arbitrary number of dimensions and for an arbitrary scalar field potential, recovering the known dispersion relation for conformal first sound.
We study the ground state instability of a strongly coupled QFT with the $z=2$ Schrödinger symmetry in a constant electric field using probe branes holography. The system is $N_f$ $\mathcal{N}=2$ hypermultiplet fermions at zero charge density in the supergravity Schrödinger background. We show that the instability occurs due to Schwinger-like effect and an insulator state will undergo a transition to a conductor state. We calculate the decay rate of instability and pair production probability by using the $gauge/gravity$ duality. At zero temperature for massive fermions, we suggest that the in…
We use holography to study finite-temperature deformations of RG flows that have exotic properties from an RG viewpoint. The holographic model consists of five-dimensional gravity coupled to a scalar field with a potential. Each negative extrema of the potential defines a dual conformal field theory. We find all the black brane solutions on the gravity side and use them to construct the thermal phase diagrams of the dual theories. We find an intricate phase structure that reflects and extends the exotic properties at zero temperature.
Using ideas from Light Front Holography, we discuss the calculation of hadronic properties. In this talk I will pay special attention to hadronic masses and the nucleon helicity-independent generalized parton distributions of quarks in the zero skewness case
Motivated by the quest for black holes in AdS braneworlds, and in particular by the holographic conjecture relating 5D classical bulk solutions with 4D quantum corrected ones, we numerically solve the semiclassical Einstein equations (backreaction equations) with matter fields in the (zero temperature) Boulware vacuum state. In the absence of an exact analytical expression for <T_(mu nu)> in four dimensions we work within the s-wave approximation. Our results show that the quantum corrected solution is very similar to Schwarzschild till very close to the horizon, but then a bouncing surface fo…
We study several aspects of charged dilaton black holes with planar symmetry in $(d+2)$-dimensional spacetime, generalizing the four-dimensional results investigated in arXiv:0911.3586 [hep-th]. We revisit the exact solutions with both zero and finite temperature and discuss the thermodynamics of the near-extremal black holes. We calculate the AC conductivity in the zero-temperature background by solving the corresponding Schrödinger equation and find that the AC conductivity behaves like $ω^δ$, where the exponent $δ$ is determined by the dilaton coupling $α$ and the spacetime dimension parame…
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…
We construct a holographic model in the framework of Q-lattices whose dual exhibits metal-insulator transitions. By introducing an interacting term between the Q-lattice and the electromagnetic field in bulk geometry, we find such kind of transition can be Mott-like. The evidences are presented as follows. i) The transition from a metallic phase to an insulating phase occurs when the lattice constant becomes larger. ii) A hard gap in the insulating phase can be manifestly observed in the optical conductivity. Nevertheless, in the zero temperature limit this model exhibits novel metallic behavi…
Quantum states with negative energy densities have been long known to exist in quantum field theories. We explore the structure of such states for holographic theories using quantum information theory tools and show how certain negative energy states are naturally captured by the thermodynamics of black holes with hyperbolic horizon at zero temperature, suggesting that they provide a dual description of those states. Our results give a satisfying field theory understanding of the distinct thermodynamics of such black holes.
We study 2+1 dimensional conformal field theories (CFTs) with a globally conserved U(1) charge, placed in a chemical potential which is periodically modulated along the spatial direction $x$ with zero average: $μ(x) = V \cos(kx)$. The dynamics of such theories depends only on the dimensionless ratio $V/k$, and we expect that they flow in the infrared to new CFTs whose universality class changes as a function of $V/k$. We compute the frequency-dependent conductivity of strongly-coupled CFTs using holography of the Einstein-Maxwell theory in 4-dimensional anti-de Sitter space. We compare the res…
We present an exactly solvable model of a scalar field in an AdS$_{d+1}$ like background interpolating between a $Z_2$ preserving and a $Z_2$ breaking minima of the potential. We define its holographic dual through the AdS/CFT dictionary and argue that at zero temperature the $d-$dimensional strongly coupled system on the boundary of AdS$_{d+1}$ exhibits a phase with a spontaneously broken discrete symmetry. In the presence of a black hole in the bulk ($T\neq 0$) we find that, although the metastable phase is present, the discrete symmetry gets restored. We compute exactly the lowest order bou…
We show that the anomalous term in the current, recently suggested by Son and Yamamoto, modifies the structure of the zero sound mode in the Fermi liquid in a magnetic field.
We find exact, analytic solutions of the Klein-Gordon equation for a scalar field in the background of the extremal Reissner-Nordstrom-AdS_5 black hole. The Green's function near a quantum critical point for a strongly coupled system can be extracted holographically from an exact solution for the scalar at zero frequency (ω), but arbitrary momentum (k), mass, and charge. By examining the Green's function near ω=0, there are two types of instability: the first one is triggered by a zero mode, and gives a hybridized critical point; the second one is triggered by the instability of the IR geometr…
Constraints on four-party entanglement in holography
University of Pennsylvania（宾夕法尼亚大学）；Vrije Universiteit Brussel（布鲁塞尔自由大学）；International Centre for Theoretical Sciences-TIFR（国际理论科学中心-印度理论研究所）；Texas A&M University（德克萨斯农工大学）；Durham University（杜伦大学）
We construct the gravity background which describes the dual field theory with aging invariance. We choose the decay modes of the bulk scalar field in the internal spectator direction to obtain the dissipative behavior of the boundary correlation functions of the dual scalar fields. In particular, the two-time correlation function at zero temperature has the characteristic features of the aging system: power law decay, broken time translation and dynamical scaling. We also construct the black hole backgrounds with asymptotic aging invariance. We extensively study characteristic behavior of the…
Inspired by a recently conjectured universal bound for thermo-electric diffusion constants in quantum critical, strongly coupled systems and relying on holographic analytical computations, we investigate the possibility of formulating Planckian bounds in different holographic models featuring momentum dissipation. For a simple massive gravity dilaton model at zero charge density we find robust linear in temperature resistivity and entropy density alongside a constant electric susceptibility. In addition we explicitly find that the sum of the thermo-electric diffusion constants is bounded.
This is a short review of recent developments in the application of AdS/CFT methods to some condensed matter problems. In particular we present the holographic description of a local quantum critical state, related to (non)-Fermi liquids and the strange metal, that appears in large N CFTs with a gravity dual at finite density and zero temperature, and explore its properties by probing it with fermionic operators. Further we discuss possible bosonic and fermionic instabilities, leading to s-, p- or d-wave holographic superconductors and "electron stars". Finally we present a realization of loca…
Using numerical holography, we study the collision, at non-zero impact parameter, of bounded, localized distributions of energy density chosen to mimic relativistic heavy ion collisions, in strongly coupled N = 4 supersymmetric Yang-Mills theory. Both longitudinal and transverse dynamics in the dual field theory are properly described. Using the gravitational description we solve 5D Einstein equations, without dimensionality reducing symmetry restrictions, to find the asymptotically anti-de Sitter spacetime geometry. Implications of our results on the understanding of early stages of heavy ion…
We study a holographic model which exhibits a quantum phase transition from the strongly interacting Weyl semimetal phase to an insulating phase. In the holographic insulating phase there is a hard gap in the real part of frequency dependent diagonal conductivities. However, the anomalous Hall conductivity is nonzero at zero frequency, indicting that it is a Chern insulator. This holographic quantum phase transition is always of first order, signified by a discontinuous anomalous Hall conductivity at the phase transition, in contrast to the very continuous holographic Weyl semimetal/trivial se…
We use holography to study sound modes of strongly-interacting conformal field theories with non-zero temperature, $T$, and $U(1)$ chemical potential, $μ$. Specifically, we consider charged black brane solutions of Einstein gravity in $(3+1)$-dimensional Anti-de Sitter space coupled to a $U(1)$ gauge field with Dirac-Born-Infeld action, representing a spacetime-filling brane. The brane action has two free parameters: the tension and the non-linearity parameter, which controls higher-order terms in the field strength. For all values of the tension, non-linearity parameter, and $T/μ$, and at suf…
We study the effects of quenched one-dimensional disorder on the holographic Weyl semimetal quantum phase transition (QPT), with a particular focus on the quantum critical region. We observe the smearing of the sharp QPT linked to the appearance of rare regions at the horizon where locally the order parameter is non-zero. We discuss the role of the disorder correlation and we compare our results to expectations from condensed matter theory at weak coupling. We analyze also the interplay of finite temperature and disorder. Within the quantum critical region we find indications for the presence …
We compute the non-zero temperature conductivity of conserved flavor currents in conformal field theories (CFTs) in 2+1 spacetime dimensions. At frequencies much greater than the temperature, $\hbarω>> k_B T$, the $ω$ dependence can be computed from the operator product expansion (OPE) between the currents and operators which acquire a non-zero expectation value at T > 0. Such results are found to be in excellent agreement with quantum Monte Carlo studies of the O(2) Wilson-Fisher CFT. Results for the conductivity and other observables are also obtained in vector 1/N expansions. We match these…
University of Heidelberg（海德堡大学）；Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute（哈里什-钱德拉研究所，霍米·巴巴国立学院成员机构）；Pontificia Universidad Católica de Valparaíso（瓦帕拉索天主教大学）；University of Ljubljana（卢布尔雅那大学）
Black hole solutions of type IIB supergravity were previously found that are dual to N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. In the zero temperature limit, these black holes approach a Liftshitz like scaling solution in the IR. It was recently shown that these black holes are unstable, and at low temperatures there is a new class of black hole solutions that are thermodynamically preferred. We extend this analysis, by considering consistent truncations of the Kaluza-Klein reduction of IIB supergravity on a five-sphere that preserves multiple scalar and $U(…
The evolution of the universe is determined by its quantum state. The wave function of the universe obeys the constraints of general relativity and in particular the Wheeler-DeWitt equation (WDWE). For non-zero Λ, we show that solutions of the WDWE at large volume have two domains in which geometries and fields are asymptotically real. In one the histories are Euclidean asymptotically anti-de Sitter, in the other they are Lorentzian asymptotically classical de Sitter. Further, the universal complex semiclassical asymptotic structure of solutions of the WDWE implies that the leading order in \h…
We construct a new class of black brane solutions in Einstein-Maxwell-dilaton (EMD) theory, which is characterized by two parameters $a,b$. Based on the obtained solutions, we make detailed analysis on the ground state in zero temperature limit and find that for many cases it exhibits the behavior of vanishing entropy density. We also find that the linear-T resistivity can be realized in a large region of temperature for the specific case of $a^2=1/3$, which is the Gubser-Rocha model dual to a ground state with vanishing entropy density. Moreover, for $a=1$ we analytically construct the black …
We discuss kinetic equations involving the anomalous terms responsible for the chiral anomaly. The general chiral heat wave in cold Fermi liquid is described and the modification of the anomalous zero sound at small temperature and vorticity is found.
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…
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…
Using simple holographic models in $D=4$ spacetime dimensions we construct black hole solutions dual to $d=3$ CFTs at finite charge density with a Q-lattice deformation. At zero temperature we find new ground state solutions with broken translation invariance, either in one or both spatial directions, which exhibit insulating or metallic behaviour depending on the parameters of the holographic theory. For low temperatures and small frequencies, the real part of the optical conductivity has a power-law behaviour, with the exponent determined by the ground state. We also obtain an expression for…
We construct a class of quantum critical points with non-mean-field critical exponents via holography. Our approach is phenomenological. Beginning with the D3/D5 system at nonzero density and magnetic field which has a chiral phase transition, we simulate the addition of a third control parameter. We then identify a line of quantum critical points in the phase diagram of this theory, provided that the simulated control parameter has dimension less than two. This line smoothly interpolates between a second-order transition with mean-field exponents at zero magnetic field to a holographic Berezi…
In this paper, we study the fate of the holographic zero sound mode at finite temperature and non-zero baryon density in the deconfined phase of the Sakai-Sugimoto model of holographic QCD. We establish the existence of such a mode for a wide range of temperatures and investigate the dispersion relation, quasi-normal modes, and spectral functions of the collective excitations in four different regimes, namely, the collisionless quantum, collisionless thermal, and two distinct hydrodynamic regimes. For sufficiently high temperatures, the zero sound completely disappears, and the low energy phys…
Microseconds after the Big Bang quarks and gluons formed a strongly-coupled non-conformal liquid driven out-of-equilibrium by the expansion of the Universe. We use holography to determine the non-equilibrium behavior of this liquid in a Friedmann-Lemaitre-Robertson-Walker Universe and develop an expansion for the corresponding entropy production in terms of the derivatives of the cosmological scale factor. We show that the resulting series has zero radius of convergence and we discuss its resurgent properties. Finally, we compute the resummed entropy production rate in de Sitter Universe at la…
We present a systematic derivation of the effective action for interacting vortices in a non-relativistic two-dimensional superfluid described by the Gross-Pitaevskii equation by integrating out longitudinal fluctuations of the order parameter. There are no logarithmically divergent coefficients in the equations of motion. Our analysis is valid in a dilute limit of vortices where the intervortex spacing is large compared to the core size, and where number fluctuations of atoms in vortex cores are suppressed. We analyze sound-induced corrections to the dynamics of a vortex-antivortex pair and s…
