We study topological modes in relativistic hydrodynamics by weakly breaking the conservation of energy momentum tensor. Several systems have been found to have topologically nontrivial crossing nodes in the spectrum of hydrodynamic modes and some of them are only topologically nontrivial with the protection of reflection symmetries in two directions. The nontrivial topology for all these systems is further confirmed from a calculation of the topological invariant. Associated transport properties and second order effects have also been studied for these systems. The non-conservation terms of the energy momentum tensor could come from an external effective symmetric tensor matter field or a gravitational field which could be generated by a specific non-inertial reference frame transformation from the original inertial reference frame. Finally we introduce a possible holographic realization of one of these systems. We propose a new method to calculate the holographic Ward identities for the energy momentum tensor without calculating out all components of the Green functions and match the Ward identities of both sides.
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 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…
The holographic interpretation of the hydrodynamic entropy current is developed for the case of hydrodynamics with a conserved charge. This is carried out within a framework developed in earlier work, which showed how to associate entropy currents with horizons in the dual geometry. The entropy current defined by the event horizon in the dual bulk geometry is calculated. It is also shown that to second order in the gradient expansion the dual geometry possesses a unique Weyl-invariant apparent horizon which also defines an admissable entropy current. At first order both currents coincide with …
We study the phenomenon of additional light waves (ALWs), observed in crystal optics: two or more electromagnetic waves with the same polarization, but different refractive index, propagate simultaneously in a isotropic medium. We show that ALWs are common in relativistic hydrodynamics, and in particular in strongly coupled systems that admit a dual gravitational description, where the ALWs are dual to quasi normal modes in the AdS gravity. We study both the transverse and the longitudinal light wave propagation. In the longitudinal channel we find a transition between regimes with different n…
We outline a program for obtaining an action principle for dissipative fluid dynamics by considering the holographic Wilsonian renormalization group applied to systems with a gravity dual. As a first step, in this paper we restrict to systems with a non-dissipative horizon. By integrating out gapped degrees of freedom in the bulk gravitational system between an asymptotic boundary and a horizon, we are led to a formulation of hydrodynamics where the dynamical variables are not standard velocity and temperature fields, but the relative embedding of the boundary and horizon hypersurfaces. At zer…
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 study the mechanisms setting the radius of convergence of hydrodynamic dispersion relations in kinetic theory in the relaxation time approximation. This introduces a qualitatively new feature with respect to holography: a nonhydrodynamic sector represented by a branch cut in the retarded Green's function. In contrast with existing holographic examples, we find that the radius of convergence in the shear channel is set by a collision of the hydrodynamic pole with a branch point. In the sound channel it is set by a pole-pole collision on a non-principal sheet of the Green's function. More gen…
We show that long-time, long-distance fluctuations of plane-symmetric horizons exhibit universal hydrodynamic behavior. By considering classical fluctuations around black-brane backgrounds, we find both diffusive and shear modes. The diffusion constant and the shear viscosity are given by simple formulas, in terms of metric components. For a given metric, the answers can be interpreted as corresponding kinetic coefficients in the holographically dual theory. For the near-extremal Dp, M2 and M5 branes, the computed kinetic coefficients coincide with the results of independent AdS/CFT calculatio…
We perform a detailed analysis of a large class of effective holographic models with broken translations at finite charge density and magnetic field. We exhaustively discuss the dispersion relations of the hydrodynamic modes at zero magnetic field and successfully match them to the predictions from charged hydrodynamics. At finite magnetic field, we identify the presence of an expected type-B Goldstone boson $\mathrm{Re}[ω]\sim k^2$, known as magnetophonon and its gapped partner -- the magnetoplasmon. We discuss their properties in relation to the effective field theory and hydrodynamics expec…
We use `generalized dimensional reduction' to relate a specific Einstein-Maxwell-Dilaton (EMD) theory, including two gauge fields, three neutral scalars and an axion, to higher-dimensional AdS gravity (with no higher-dimensional Maxwell field). In general, this is a dimensional reduction over compact Einstein spaces in which the dimension of the compact space is continued to non-integral values. Specifically, we perform a non-diagonal Kaluza-Klein (KK) reduction over a torus, involving two KK gauge fields. Our aim is to determine the holographic dictionary and hydrodynamic behaviour of the low…
We consider second-order viscous hydrodynamics in conformal field theories at finite temperature. We show that conformal invariance imposes powerful constraints on the form of the second-order corrections. By matching to the AdS/CFT calculations of correlators, and to recent results for Bjorken flow obtained by Heller and Janik, we find three (out of five) second-order transport coefficients in the strongly coupled N=4 supersymmetric Yang-Mills theory. We also discuss how these new coefficents can arise within the kinetic theory of weakly coupled conformal plasmas. We point out that the Muelle…
We calculate the free energy from the on-shell action for topologically massive gravity with negative and vanishing cosmological constant, thereby providing a first principles derivation of the free energy of Banados-Teitelboim-Zanelli (BTZ) black holes and flat space cosmologies. We summarize related recent checks of flat space holography.
In this Colloquium, we review recent progress in the effective description of strongly-correlated phases of matter with spontaneously broken translations, such as charge density waves or Wigner crystals. In real materials, disorder is inevitable and pins the Goldstones of broken translations. We describe how pinning can be incorporated in the effective field theory at low energies, without making any assumption on the presence of boost symmetry. We review the essential role played by gauge-gravity duality models in establishing these effective field theories with only approximate symmetries. W…
We study the convergence of the hydrodynamic series in the gravity dual of Gauss-Bonnet gravity in five dimensions with negative cosmological constant via holography. By imposing boost invariance symmetry, we find a solution to the Gauss-Bonnet equation of motion in inverse powers of the proper time, from which we can extract high order corrections to Bjorken flow for different values of the Gauss-Bonnet parameter $λ_{GB}$. As in all other known examples the gradient expansion is, at most, an asymptotic series which can be understood through applying the techniques of Borel-Padé summation. As …
We discuss the stability of the topological invariant of the strongly interacting Weyl semi-metal at finite temperature. We find that if the interactions and temperature of the system are controlled by the holography, the topology is stable even in the case the Fermi surface become fuzzy. We give an argument to show that although the self energy changes the spectral function significantly to make the Fermi surface fuzzy, it cannot change the singularity structure of the Berry phase, which leads to the stability of the topology. We also find that depending on the mass term structure of the ferm…
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…
In four dimensions Weyl fermions possess a chiral anomaly which leads to several special features in the transport phenomena, such as the negative longitudinal magnetoresistivity. In this paper, we study its inverse, the longitudinal magnetoconductivity, in the case of a chiral anomalous system with a background magnetic field B using the linear response method in the hydrodynamic limit and from holography. Our hydrodynamic results show that in general we need to have energy, momentum and charge dissipations to get a finite DC longitudinal magnetoconductivity due to the existence of the chiral…
We show a holographic model of a strongly coupled topological nodal line semimetal (NLSM) and find that the NLSM phase could go through a quantum phase transition to a topologically trivial state. The dual fermion spectral function shows that there are multiple Fermi surfaces each of which is a closed nodal loop in the NLSM phase. The topological structure in the bulk is induced by the IR interplay between the dual mass operator and the operator that deforms the topology of the Fermi surface. We propose a practical framework for building various strongly coupled topological semimetals in holog…
Topological entanglement entropy, a measure of the long-ranged entanglement, is related to the degeneracy of the ground state on a higher genus surface. The exact relation depends on the details of the topological theory. We consider a class of holographic models where such relation might be similar to the one exhibited by Chern-Simons theory in a certain large N limit. Both the non-vanishing topological entanglement entropy and the ground state degeneracy in these holographic models are consequences of the topological Gauss-Bonnet term in the dual gravitational description. A soft wall hologr…
We formulate the theory of nonlinear viscoelastic hydrodynamics of anisotropic crystals in terms of dynamical Goldstone scalars of spontaneously broken translational symmetries, under the assumption of homogeneous lattices and absence of plastic deformations. We reformulate classical elasticity effective field theory using surface calculus in which the Goldstone scalars naturally define the position of higher-dimensional crystal cores, covering both elastic and smectic crystal phases. We systematically incorporate all dissipative effects in viscoelastic hydrodynamics at first order in a long-w…
A new topological conformal field theory in four Euclidean dimensions is constructed from N=4 super Yang-Mills theory by twisting the whole of the conformal group with the whole of the R-symmetry group, resulting in a theory that is conformally invariant and has two conformally invariant BRST operators. A curved space generalisation is found on any Riemannian 4-fold. This formulation has local Weyl invariance and two Weyl-invariant BRST symmetries, with an action and energy-momentum tensor that are BRST-exact. This theory is expected to have a holographic dual in 5-dimensional de Sitter space.
AdS black holes with planar event horizon topology play a central role in AdS/CFT holography, and particularly in its applications. Generalisations of the known planar black holes can be found by considering the Plebanski--Demianski metrics, a very general family of exactly specified solutions of the Einstein equations. These generalised planar black holes may be useful in applications. We give a concrete example of this in the context of the holographic description of the Quark-Gluon Plasma (QGP). We argue that our generalised planar black holes allow us to construct a model of the internal s…
We analyse a simple example of a holographically dual pair in which we topologically twist both theories. The holography is based on the two-dimensional N=2 supersymmetric Liouville conformal field theory that defines a unitary bulk quantum supergravity theory in three-dimensional anti-de Sitter space. The supersymmetric version of three-dimensional Liouville quantum gravity allows for a topological twist on the boundary and in the bulk. We define the topological bulk supergravity theory in terms of twisted boundary conditions. We corroborate the duality by calculating the chiral configuration…
We investigate the low-energy dynamics of systems with pseudo-spontaneously broken $U(1)$ symmetry and Goldstone phase relaxation. We construct a hydrodynamic framework which is able to capture these, in principle independent, effects. We consider two generalisations of the standard holographic superfluid model by adding an explicit breaking of the $U(1)$ symmetry by either sourcing the charged bulk scalar or by introducing an explicit mass term for the bulk gauge field. We find agreement between the hydrodynamic dispersion relations and the quasi-normal modes of both holographic models. We ve…
We present a holographic model of a topological Weyl semimetal. A key ingredient is a time-reversal breaking parameter and a mass deformation. Upon varying the ratio of mass to time-reversal breaking parameter the model undergoes a quantum phase transition from a topologically nontrivial semimetal to a trivial one. The topological nontrivial semimetal is characterised by the presence of an anomalous Hall effect. The results can be interpreted in terms of the holographic renormalization group (RG) flow leading to restoration of time-reversal at the end point of the RG flow in the trivial phase.
Hydrodynamics is a theory of long-range excitations controlled by equations of motion that encode the conservation of a set of currents (energy, momentum, charge, etc.) associated with explicitly realized global symmetries. If a system possesses additional weakly broken symmetries, the low-energy hydrodynamic degrees of freedom also couple to a few other "approximately conserved" quantities with parametrically long relaxation times. It is often useful to consider such approximately conserved operators and corresponding new massive modes within the low-energy effective theory, which we refer to…
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 derive and test a novel holographic duality in the B-model topological string theory. The duality relates the B-model on certain Calabi-Yau three-folds to two-dimensional chiral algebras defined as gauged $βγ\,$ systems. The duality conjecturally captures a topological sector of more familiar $\mathrm{AdS}_5 / \mathrm{CFT}_4$ holographic dualities.
Entropic order parameters and topological holography
Instituto de Física Teórica UAM/CSIC（UAM/CSIC理论物理研究所）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Universidad Politécnica de Cartagena（卡塔赫纳理工大学）
We examine the formation and critical dynamics of topological defects via Kibble-Zurek mechanism in a (2+1)-dimensional quantum critical point, which is conjectured to dual to a Lifshitz geometry. Quantized magnetic fluxoids are spontaneously generated and trapped in the cores of order parameter vortices, which is a feature of type II superconductors. Time evolution of the average condensate is found to lag behind the instantaneous equilibrium value of the order parameter, a typical phenomenon in nonequilibrium dynamics. Scalings of vortex number density and the "freeze-out" time match the pre…
We study the chiral vortical conductivity in a holographic Weyl semimetal model, which describes a topological phase transition from the strongly coupled topologically nontrivial phase to a trivial phase. We focus on the temperature dependence of the chiral vortical conductivity where the mixed gauge-gravitational anomaly plays a crucial role. After a proper renormalization of the chiral vortical conductivity by the anomalous Hall conductivity and temperature squared, we find that at low temperature in both the Weyl semimetal phase and the quantum critical region this renormalized ratio stays …
We investigate effects of strong correlation on the surface state of topological insulator (TI). We argue that electrons in the regime of crossover from weak anti-localization to weak localization, are strongly correlated and calculate magneto-transport coefficients of TI using gauge gravity principle. Then, we examine, magneto-conductivity (MC) formula and find excellent agreement with the data of chrome doped Bi$_{2}$Te$_{3}$ in the crossover regime. We also find that cusp-like peak in MC at low doping is absent, which is natural since quasi-particles disappear due to the strong correlation.
Motivated by the physics of the quark-gluon plasma created in heavy-ion collision experiments, we use holography to study the regime of applicability of various theories of relativistic viscous hydrodynamics. Using the microscopic description provided by holography of a system that relaxes to equilibrium, we obtain initial data with which we perform real-time evolutions in 2+1 dimensional conformal fluids using the first-order viscous relativistic hydrodynamics theory of Bemfica, Disconzi, Noronha and Kovtun (BDNK), BRSSS and ideal hydrodynamics. By initializing the hydrodynamics codes at diff…
The fluid-gravity correspondence provides us with explicit spacetime metrics that are holographically dual to (non-)relativistic nonlinear hydrodynamics. The vacuum Einstein equations, in the presence of a Killing vector, possess solution-generating symmetries known as spacetime Ehlers transformations. These form a subgroup of the larger generalized Ehlers group acting on spacetimes with arbitrary matter content. We apply this generalized Ehlers group, in the presence of Killing isometries, to vacuum metrics with hydrodynamic duals to develop a formalism for solution-generating transformations…
We investigate the thermodynamics of AdS black holes in Generalized Quasitopological Gravity with and without electric charge, concentrating on the version of the theory that is cubic in curvature. We study new aspects of Hawking-Page transitions that occur for these black holes. Working within the framework of black hole chemistry, we find a variety of familiar and new critical behaviour and phase transitions in four and higher dimensions for the charged black holes. We also consider some holographic aspects of our work, demonstrating how the ratio of viscosity to entropy is modified by inclu…
We study a topological field theory in four dimensions on a manifold with boundary. A bulk-boundary interaction is introduced through a novel variational principle rather than explicitly. Through this scheme we find that the boundary values of the bulk fields act as external sources for the boundary theory. Furthermore, the full quantum states of the theory factorize into a single bulk state and an infinite number of boundary states labeled by loops on the spatial boundary. In this sense the theory is purely holographic. We show that this theory is dual to Chern-Simons theory with an external …
In the course of the past several years holography has emerged as an ab initio tool in exploring strongly-time-dependent phenomena in gauge theories. These lecture notes overview recent developments in this area driven by phenomenological questions concerning applicability of hydrodynamics (hydrodynamization) under extreme conditions occurring in ultrarelativistic heavy-ion collisions at RHIC and LHC. The topics include hydrodynamization time scale, holographic collisions, as well as hydrodynamization from the point of view of the asymptotic character of the hydrodynamic gradient expansion. Th…
In this paper, we derive the field equations of quartic quasi-topological gravity by varying the action with respect to the metric. Also, we obtain the linearized graviton equations in the AdS background and find that it is governed by a second-order field equation as in the cases of Einstein, Lovelock or cubic quasi-topological gravities. But in contrast to the cubic quasi-topological gravity, the linearized field equation around a black hole has fourth-order radial derivative of the perturbation. Moreover, we analyze the conditions of having ghost free AdS solutions and AdS planar black hole…
We study phase transitions in five-dimensional Einstein Gravity with a negative cosmological constant, coupled to a Skyrme matter field. These transitions are topological generalizations of the Hawking-Page transition between thermal Anti de Sitter (AdS) spacetime and an AdS black hole. Phases are characterized by a topological number associated with the Skyrme field configuration. Depending on that topological number and on the Skyrme coupling strength, there occur transitions between those phases at two, one, or no value(s) of the temperature. Through the holographic (AdS/CFT) correspondence…
We propose an explicit realization of flat space holography in two dimensions where both sides of the duality are independently defined and the boundary theory is completely solvable. In the bulk, we define a novel $\mathcal{N}=1$ flat space supergravity theory and exactly compute the full topological expansion of its Euclidean partition function with an arbitrary number of boundaries. On the boundary, we consider a double scaled Hermitian random matrix model with Gaussian potential and use the loop equations to show it independently reproduces the bulk partition function to all orders in the …
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…
We report on the approach towards the hydrodynamic regime of boost-invariant N=4 super Yang-Mills plasma at strong coupling starting from various far-from-equilibrium states at tau=0. The results are obtained through numerical solution of Einstein's equations for the dual geometries, as described in detail in the companion article arXiv:1203.0755. Despite the very rich far-from-equilibrium evolution, we find surprising regularities in the form of clear correlations between initial entropy and total produced entropy, as well as between initial entropy and the temperature at thermalization, unde…
Recently it has been suggested that non-gaussian inflationary perturbations can be usefully analysed in terms of a putative dual gauge theory defined on the future conformal infinity generated by an accelerating cosmology. The problem is that unitarity of this gauge theory implies a strong constraint [the "Strominger bound"] on the matter fields in the bulk. We argue that the bound is just a reflection of the equation of state of cosmological matter. The details motivate a discussion of the possible relevance of the ``dS/CFT correspondence" to the resolution of the Big Bang singularity. It is …
