These are notes based on a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided to the extent possible.

Holographic Duality with a View Toward Many-Body Physics

We present a review of theories of states of quantum matter without quasiparticle excitations. Solvable examples of such states are provided through a holographic duality with gravitational theories in an emergent spatial dimension. We review the duality between gravitational backgrounds and the various states of quantum matter which live on the boundary. We then describe quantum matter at a fixed commensurate density (often described by conformal field theories), and also compressible quantum matter with variable density, providing an extensive discussion of transport in both cases. We present a unified discussion of the holographic theory of transport with memory matrix and hydrodynamic methods, allowing a direct connection to experimentally realized quantum matter. We also explore other important challenges in non-quasiparticle physics, including symmetry broken phases such as superconductors and non-equilibrium dynamics.

Holographic Quantum Matter

Efficient momentum relaxation through umklapp scattering, leading to a power law in temperature dc resistivity, requires a significant low energy spectral weight at finite momentum. One way to achieve this is via a Fermi surface structure, leading to the well-known relaxation rate Γ∼T2. We observe that local criticality, in which energies scale but momenta do not, provides a distinct route to efficient umklapp scattering. We show that umklapp scattering by an ionic lattice in a locally critical theory leads to Γ∼T(2Δ(k(L))). Here Δ(k(L))≥0 is the dimension of the (irrelevant or marginal) charge density operator J(t)(ω,k(L)) in the locally critical theory, at the lattice momentum k(L). We illustrate this result with an explicit computation in locally critical theories described holographically via Einstein-Maxwell theory in Anti-de Sitter spacetime. We furthermore show that scattering by random impurities in these locally critical theories gives a universal Γ∼(log(1/T))(-1).

Locally Critical Resistivities from Umklapp Scattering

Ten years ago, relativistic viscous fluid dynamics was formulated from first principles in an effective field theory framework, based entirely on the knowledge of symmetries and long-lived degrees of freedom. In the same year, numerical simulations for the matter created in relativistic heavy-ion collision experiments became first available, providing constraints on the shear viscosity in QCD. The field has come a long way since then. We present the current status of the theory of non-equilibrium fluid dynamics in 2017, including the divergence of the fluid dynamic gradient expansion, resurgence, non-equilibrium attractor solutions, the inclusion of thermal fluctuations as well as their relation to microscopic theories. Furthermore, we review the theory basis for numerical fluid dynamics simulations of relativistic nuclear collisions, and comparison of modern simulations to experimental data for nucleus-nucleus, nucleus-proton and proton-proton collisions.

Relativistic Fluid Dynamics In and Out of Equilibrium -- Ten Years of Progress in Theory and Numerical Simulations of Nuclear Collisions

The bulk motion of nuclear matter at the ultrahigh temperatures created in heavy ion collisions at the Relativistic Heavy Ion Collider and the Large Hadron Collider is well described in terms of ne...

https://www.annualreviews.org/doi/pdf/10.1146/annurev-nucl-101916-123209

Small System Collectivity in Relativistic Hadronic and Nuclear Collisions

Hydrodynamics can be formulated as the gradient expansion of conserved currents in terms of the fundamental fields describing the near-equilibrium fluid flow. In the relativistic case, the Navier-Stokes equations follow from the conservation of the stress-energy tensor to first order in derivatives. In this paper, we go beyond the presently understood second-order hydrodynamics and discuss the systematization of obtaining the hydrodynamic expansion to an arbitrarily high order. As an example of the algorithm that we present, we fully classify the gradient expansion at third order for neutral fluids in four dimensions, thus finding the most general next-to-leading-order corrections to the relativistic Navier-Stokes equations in curved space-time. In doing so, we list 20 new transport coefficient candidates in the conformal case and 68 in the nonconformal case. As we do not consider any constraints that could potentially arise from the local entropy current analysis, this is the maximal possible set of neutral third-order transport coefficients. To investigate the physical implications of these new transport coefficients, we obtain the third-order corrections to the linear dispersion relations that describe the propagation of diffusion and sound waves in relativistic fluids. We also compute the corrections to the scalar (spin-2) two-point correlation function of the third-order stress-energy tensor. Furthermore, as an example of a nonlinear hydrodynamic flow, we calculate the third-order corrections to the energy density of a boost-invariant Bjorken flow. Finally, we apply our field theoretic results to the $\mathcal{N}=4$ supersymmetric Yang-Mills fluid at infinite 't Hooft coupling and an infinite number of colors to find the values of five new linear combinations of the conformal transport coefficients.

Constructing higher-order hydrodynamics: The third order.

We investigate the analytic structure of thermal energy-momentum tensor correlators at large but finite coupling in quantum field theories with gravity duals. We compute corrections to the quasinormal spectra of black branes due to the presence of higher derivative R
 2 and R
 4 terms in the action, focusing on the dual to $$ \mathcal{N}=4 $$
 SYM theory and Gauss-Bonnet gravity. We observe the appearance of new poles in the complex frequency plane at finite coupling. The new poles interfere with hydrodynamic poles of the correlators leading to the breakdown of hydrodynamic description at a coupling-dependent critical value of the wave-vector. The dependence of the critical wave vector on the coupling implies that the range of validity of the hydrodynamic description increases monotonically with the coupling. The behavior of the quasinormal spectrum at large but finite coupling may be contrasted with the known properties of the hierarchy of relaxation times determined by the spectrum of a linearized kinetic operator at weak coupling. We find that the ratio of a transport coefficient such as viscosity to the relaxation time determined by the fundamental non-hydrodynamic quasinormal frequency changes rapidly in the vicinity of infinite coupling but flattens out for weaker coupling, suggesting an extrapolation from strong coupling to the kinetic theory result. We note that the behavior of the quasinormal spectrum is qualitatively different depending on whether the ratio of shear viscosity to entropy density is greater or less than the universal, infinite coupling value of ℏ/4πk
 B . In the former case, the density of poles increases, indicating a formation of branch cuts in the weak coupling limit, and the spectral function shows the appearance of narrow peaks. We also discuss the relation of the viscosity-entropy ratio to conjectured bounds on relaxation time in quantum systems.

/pdf/from-strong-to-weak-coupling-in-holographic-models-of-2g55byiv6y.pdf

From strong to weak coupling in holographic models of thermalization

We study the long-lived modes of the charge density and energy density correla- tors in the strongly-coupled, finite density field theory dual to the AdS
 4 Reissner-Nordstrom black hole. For small momenta $ q \ll \mu $
 , these correlators contain a pole due to sound propagation, as well as a pole due to a long-lived, purely imaginary mode analogous to the μ = 0 hydrodynamic charge diffusion mode. As the temperature is raised in the range $ T{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{ < }}\mu $
 , the sound attenuation shows no significant temperature dependence. When $ T{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{ > }}\mu $
 , it quickly approaches the μ = 0 hydrodynamic result where it decreases like 1/T. It does not share any of the temperature-dependent properties of the ‘zero sound’ of Landau Fermi liquids observed in the strongly-coupled D3/D7 field theory. For such small momenta, the energy density spectral function is dominated by the sound mode at all temperatures, whereas the charge density spectral function undergoes a crossover from being dominated by the sound mode at low temperatures to being dominated by the diffusion mode when $ T \sim {\mu^2}/q $
 . This crossover occurs due to the changing residue at each pole. We also compute the momentum dependence of these spectral functions and their corresponding long-lived poles at fixed, low temperatures $ T \ll \mu $
 .

Bosonic excitations of the AdS 4 Reissner-Nordstrom black hole

We study the long-lived modes of the charge density and energy density correlators in the strongly-coupled, finite density field theory dual to the AdS4 Reissner-Nordstrom black hole. For small momenta q<<\mu, these correlators contain a pole due to sound propagation, as well as a pole due to a long-lived, purely imaginary mode analogous to the \mu=0 hydrodynamic charge diffusion mode. As the temperature is raised in the range T\lesssim\mu, the sound attenuation shows no significant temperature dependence. When T\gtrsim\mu, it quickly approaches the \mu=0 hydrodynamic result where it decreases like 1/T. It does not share any of the temperature-dependent properties of the 'zero sound' of Landau Fermi liquids observed in the strongly-coupled D3/D7 field theory. For such small momenta, the energy density spectral function is dominated by the sound mode at all temperatures, whereas the charge density spectral function undergoes a crossover from being dominated by the sound mode at low temperatures to being dominated by the diffusion mode when T \mu^2/q. This crossover occurs due to the changing residue at each pole. We also compute the momentum dependence of these spectral functions and their corresponding long-lived poles at fixed, low temperatures T<<\mu.

Bosonic excitations of the AdS4 Reissner-Nordstrom black hole

Social media communications are becoming increasingly prevalent; some useful, some false, whether unwittingly or maliciously. An increasing number of rumours daily flood the social networks. Determining their veracity in an autonomous way is a very active and challenging field of research, with a variety of methods proposed. However, most of the models rely on determining the constituent messages’ stance towards the rumour, a feature known as the “wisdom of the crowd.” Although several supervised machine-learning approaches have been proposed to tackle the message stance classification problem, these have numerous shortcomings. In this paper, we argue that semi-supervised learning is more effective than supervised models and use two graph-based methods to demonstrate it. This is not only in terms of classification accuracy, but equally important, in terms of speed and scalability. We use the Label Propagation and Label Spreading algorithms and run experiments on a dataset of 72 rumours and hundreds of thousands messages collected from Twitter. We compare our results on two available datasets to the state-of-the-art to demonstrate our algorithms’ performance regarding accuracy, speed, and scalability for real-time applications.

/pdf/a-semi-supervised-approach-to-message-stance-classification-58tedrqwka.pdf

Nikolaos Kaplis

Papers

Constructing higher-order hydrodynamics: The third order.

From strong to weak coupling in holographic models of thermalization

Bosonic excitations of the AdS 4 Reissner-Nordstrom black hole

Bosonic excitations of the AdS4 Reissner-Nordstrom black hole

A Semi-Supervised Approach to Message Stance Classification