arXiv subjects

Sašo Grozdanov

Publications and source records attributed to Sašo Grozdanov.

At least 55 records · Page 3Linked to original sources

arXiv2018

Generalised global symmetries in states with dynamical defects: the case of the transverse sound in field theory and holography

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 with spontaneous breaking of translational symmetry caused by the underlying microscopic structure---the principle feature of which is a transverse sound mode. At the linear, non-dissipative level, we verify that our theory, based entirely on symmetry principles, is equivalent to a viscoelastic theory. We then build a simple holographic dual of such a state containing dynamical gravity and two two-form gauge fields, and use it to study its hydrodynamic and higher-energy spectral properties characterised by non-hydrodynamic, gapped modes. Based on the holographic analysis of transverse two-point functions, we study consistency between low-energy predictions of the bulk theory and the effective boundary theory. Various new features of the holographic dictionary are explained in theories with higher-form symmetries, such as the mixed-boundary-condition modification of the quasinormal mode prescription that depends on the running coupling of the boundary double-trace deformations. Furthermore, we examine details of low- and high-energy parts of the spectrum that depend on temperature, line defect densities and the renormalisation group scale.

hep-th↗

arXiv2018

Black hole scrambling from hydrodynamics

We argue that the gravitational shock wave computation used to extract the scrambling rate in strongly coupled quantum theories with a holographic dual is directly related to probing the system's hydrodynamic sound modes. The information recovered from the shock wave can be reconstructed in terms of purely diffusion-like, linearized gravitational waves at the horizon of a single-sided black hole with specific regularity-enforced imaginary values of frequency and momentum. In two-derivative bulk theories, this horizon "diffusion" can be related to late-time momentum diffusion via a simple relation, which ceases to hold in higher-derivative theories. We then show that the same values of imaginary frequency and momentum follow from a dispersion relation of a hydrodynamic sound mode. The frequency, momentum and group velocity give the holographic Lyapunov exponent and the butterfly velocity. Moreover, at this special point along the sound dispersion relation curve, the residue of the retarded longitudinal stress-energy tensor two-point function vanishes. This establishes a direct link between a hydrodynamic sound mode at an analytically continued, imaginary momentum and the holographic butterfly effect. Furthermore, our results imply that infinitely strongly coupled, large-$N_c$ holographic theories exhibit properties similar to classical dilute gasses; there, late-time equilibration and early-time scrambling are also controlled by the same dynamics.

hep-th↗

arXiv2017

Holographic constraints on Bjorken hydrodynamics at finite coupling

In large-$N_c$ conformal field theories with classical holographic duals, inverse coupling constant corrections are obtained by considering higher-derivative terms in the corresponding gravity theory. In this work, we use type IIB supergravity and bottom-up Gauss-Bonnet gravity to study the dynamics of boost-invariant Bjorken hydrodynamics at finite coupling. We analyze the time-dependent decay properties of non-local observables (scalar two-point functions and Wilson loops) probing the different models of Bjorken flow and show that they can be expressed generically in terms of a few field theory parameters. In addition, our computations provide an analytically quantifiable probe of the coupling-dependent validity of hydrodynamics at early times in a simple model of heavy-ion collisions, which is an observable closely analogous to the hydrodynamization time of a quark-gluon plasma. We find that to third order in the hydrodynamic expansion, the convergence of hydrodynamics is improved and that generically, as expected from field theory considerations and recent holographic results, the applicability of hydrodynamics is delayed as the field theory coupling decreases.

hep-th↗

arXiv2017

Constructing higher-order hydrodynamics: The third order

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 systematisation 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 and $68$ in the non-conformal 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 non-linear 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 infinite number of colours to find the values of five new linear combinations of the conformal transport coefficients.

hep-th↗

arXiv2017

Coupling constant corrections in a holographic model of heavy ion collisions

We initiate a holographic study of coupling-dependent heavy ion collisions by analysing for the first time the effects of leading-order, inverse coupling constant corrections. In the dual description, this amounts to colliding gravitational shock waves in a theory with curvature-squared terms. We find that at intermediate coupling, nuclei experience less stopping and have more energy deposited near the lightcone. When the decreased coupling results in an 80% larger shear viscosity, the time at which hydrodynamics becomes a good description of the plasma created from high energy collisions increases by 25%. The hydrodynamic phase of the evolution starts with a wider rapidity profile and smaller entropy.

hep-th↗

arXiv2017

Generalized global symmetries and dissipative magnetohydrodynamics

The conserved magnetic flux of U(1) electrodynamics coupled to matter in four dimensions is associated with a generalized global symmetry. We study the realization of such a symmetry at finite temperature and develop the hydrodynamic theory describing fluctuations of a conserved 2-form current around thermal equilibrium. This can be thought of as a systematic derivation of relativistic magnetohydrodynamics, constrained only by symmetries and effective field theory. We construct the entropy current and show that at first order in derivatives, there are seven dissipative transport coefficients. We present a universal definition of resistivity in a theory of dynamical electromagnetism and derive a direct Kubo formula for the resistivity in terms of correlation functions of the electric field operator. We also study fluctuations and collective modes, deriving novel expressions for the dissipative widths of magnetosonic and Alfven modes. Finally, we demonstrate that a non-trivial truncation of the theory can be performed at low temperatures compared to the magnetic field: this theory has an emergent Lorentz invariance along magnetic field lines, and hydrodynamic fluctuations are now parametrized by a fluid tensor rather than a fluid velocity. Throughout, no assumption is made of weak electromagnetic coupling. Thus, our theory may have phenomenological relevance for dense electromagnetic plasmas.

hep-th↗

arXiv2017

Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid

Gauss-Bonnet holographic fluid is a useful theoretical laboratory to study the effects of curvature-squared terms in the dual gravity action on transport coefficients, quasinormal spectra and the analytic structure of thermal correlators at strong coupling. To understand the behavior and possible pathologies of the Gauss-Bonnet fluid in $3+1$ dimensions, we compute (analytically and non-perturbatively in the Gauss-Bonnet coupling) its second-order transport coefficients, the retarded two- and three-point correlation functions of the energy-momentum tensor in the hydrodynamic regime as well as the relevant quasinormal spectrum. The Haack-Yarom universal relation among the second-order transport coefficients is violated at second order in the Gauss-Bonnet coupling. In the zero-viscosity limit, the holographic fluid still produces entropy, while the momentum diffusion and the sound attenuation are suppressed at all orders in the hydrodynamic expansion. By adding higher-derivative electromagnetic field terms to the action, we also compute corrections to charge diffusion and identify the non-perturbative parameter regime in which the charge diffusion constant vanishes.

hep-th↗

arXiv2017

Weak Quantum Chaos

Out-of-time-ordered correlation functions (OTOC's) are presently being extensively debated as quantifiers of dynamical chaos in interacting quantum many-body systems. We argue that in quantum spin and fermionic systems, where all local operators are bounded, an OTOC of local observables is bounded as well and thus its exponential growth is merely transient. As a better measure of quantum chaos in such systems, we propose, and study, the density of the OTOC of extensive sums of local observables, which can exhibit indefinite growth in the thermodynamic limit. We demonstrate this for the kicked quantum Ising model by using large-scale numerical results and an analytic solution in the integrable regime. In a generic case, we observe the growth of the OTOC density to be linear in time. We prove that this density in general, locally interacting, non-integrable quantum spin and fermionic dynamical systems exhibits growth that is at most polynomial in time---a phenomenon, which we term weak quantum chaos. In the special case of the model being integrable and the observables under consideration quadratic, the OTOC density saturates to a plateau.

cond-mat.stat-mech↗

arXiv2017

Momentum and charge transport in non-relativistic holographic fluids from Hořava gravity

We study the linearized transport of transverse momentum and charge in a conjectured field theory dual to a black brane solution of Horava gravity with Lifshitz exponent $z=1$. As expected from general hydrodynamic reasoning, we find that both of these quantities are diffusive over distance and time scales larger than the inverse temperature. We compute the diffusion constants and conductivities of transverse momentum and charge, as well the ratio of shear viscosity to entropy density, and find that they differ from their relativistic counterparts. To derive these results, we propose how the holographic dictionary should be modified to deal with the multiple horizons and differing propagation speeds of bulk excitations in Horava gravity. When possible, as a check on our methods and results, we use the covariant Einstein-Aether formulation of Horava gravity, along with field redefinitions, to re-derive our results from a relativistic bulk theory.

hep-th↗

arXiv2017

On the universal identity in second order hydrodynamics

We compute the 't Hooft coupling correction to the infinite coupling expression for the second order transport coefficient $λ_2$ in ${\cal N}=4$ $SU(N_c)$ supersymmetric Yang-Mills theory at finite temperature in the limit of infinite $N_c$, which originates from the $R^4$ terms in the low energy effective action of the dual type IIB string theory. Using this result, we show that the identity involving the three second order transport coefficients, $2 ητ_Π- 4 λ_1 - λ_2 =0$, previously shown by Haack and Yarom to hold universally in relativistic conformal field theories with string dual descriptions to leading order in supergravity approximation, holds also at next to leading order in this theory. We also compute corrections to transport coefficients in a (hypothetical) strongly interacting conformal fluid arising from the generic curvature squared terms in the corresponding dual gravity action (in particular, Gauss-Bonnet action), and show that the identity holds to linear order in the higher-derivative couplings. We discuss potential implications of these results for the near-equilibrium entropy production rate at strong coupling.

hep-th↗

arXiv2016

Universality of anomalous conductivities in theories with higher-derivative holographic duals

Anomalous chiral conductivities in theories with global anomalies are independent of whether they are computed in a weakly coupled quantum (or thermal) field theory, hydrodynamics, or at infinite coupling from holography. While the presence of dynamical gauge fields and mixed, gauge-global anomalies can destroy this universality, in their absence, the non-renormalisation of anomalous Ward identities is expected to be obeyed at all intermediate coupling strengths. In holography, bulk theories with higher-derivative corrections incorporate coupling constant corrections to the boundary theory observables in an expansion around infinite coupling. In this work, we investigate the coupling constant dependence and universality of anomalous conductivities (and thus of the anomalous Ward identities) in general, four-dimensional systems that possess asymptotically anti-de Sitter holographic duals with a non-extremal black brane in five dimensions, and anomalous transport introduced into the boundary theory via the bulk Chern-Simons action. We show that in bulk theories with arbitrary gauge- and diffeomorphism-invariant higher-derivative actions, anomalous conductivities, which can incorporate an infinite series of (inverse) coupling constant corrections, remain universal. Owing to the existence of the membrane paradigm, the proof reduces to a construction of bulk effective theories at the horizon and the boundary. It only requires us to impose the condition of horizon regularity and correct boundary conditions on the fields. We also discuss ways to violate the universality by violating conditions for the validity of the membrane paradigm, in particular, by adding mass to the vector fields (a case with a mixed, gauge-global anomaly) and in bulk geometries with a naked singularity.

hep-th↗

arXiv2016

Inflationary Potentials from the Exact Renormalisation Group

We show that an inflationary slow-roll potential can be derived as an IR limit of the non-perturbative exact renormalisation group equation for a scalar field within the mean-field approximation. The result follows without having to specify a Lagrangian for the UV theory at the Planck scale. We assume that the theory contains a scalar mode with suppressed coupling to other UV fields, and that higher derivative couplings are suppressed. The resulting effective potential gives rise to slow-roll inflation, which is fully consistent with the recent observations. As an example of how the proposed renormalisation group procedure works, we perform an explicit calculation in the $ϕ^4$ theory.

hep-th↗

arXiv2016

From strong to weak coupling in holographic models of thermalization

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 $\hbar/4πk_B$. 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.

hep-th↗

arXiv2016

Incoherent thermal transport from dirty black holes

We study thermal transport in strongly disordered, strongly interacting quantum field theories without quasiparticles using gauge-gravity duality. We analyze linear perturbations of black holes with broken translational symmetry in Einstein-Maxwell-dilaton theories of gravity. Using general geometric arguments in the bulk, we derive bounds on thermal conductivity for the dual disordered field theories in one and two spatial dimensions. In the latter case, the thermal conductivity is always non-zero at finite temperature, so long as the dilaton potential is bounded from below. Hence, generic holographic models make non-trivial predictions about the thermal conductivity in a strongly disordered, strongly coupled metal in two spatial dimensions.

hep-th↗

arXiv2015

Absence of disorder-driven metal-insulator transitions in simple holographic models

We study electrical transport in a strongly coupled strange metal in two spatial dimensions at finite temperature and charge density, holographically dual to Einstein-Maxwell theory in an asymptotically $\mathrm{AdS}_4$ spacetime, with arbitrary spatial inhomogeneity, up to mild assumptions including emergent isotropy. In condensed matter, these are candidate models for exotic strange metals without long-lived quasiparticles. We prove that the electrical conductivity is bounded from below by a universal minimal conductance: the quantum critical conductivity of a clean, charge-neutral plasma. Beyond non-perturbatively justifying mean-field approximations to disorder, our work demonstrates the practicality of new hydrodynamic insight into holographic transport.

hep-th↗

arXiv2015

Dynamics of the electric current in an ideal electron gas: a sound mode inside the quasi-particles

We study the equation of motion for the Noether current in an electron gas within the framework of the Schwinger-Keldysh Closed-Time-Path formalism. The equation is shown to be highly non-linear and irreversible even for a non-interacting, ideal gas of electrons at non-zero density. We truncate the linearised equation of motion, written as the Laurent series in Fourier space, so that the resulting expressions are local in time, both at zero and at small finite temperatures. Furthermore, we show that the one-loop Coulomb interactions only alter the physical picture quantitatively, while preserving the characteristics of the dynamics that the electric current exhibits in the absence of interactions. As a result of the composite nature of the Noether current, {\it composite sound} waves are found to be the dominant IR collective excitations at length scales between the inverse Fermi momentum and the mean free path that would exist in an interacting electron gas. We also discuss the difference and the transition between the hydrodynamical regime of an ideal gas, defined in this work, and the hydrodynamical regime in phenomenological hydrodynamics, which is normally used for the description of interacting gases.

hep-th↗

arXiv2015

Viscosity and dissipative hydrodynamics from effective field theory

With the goal of deriving dissipative hydrodynamics from an action, we study classical actions for open systems, which follow from the generic structure of effective actions in the Schwinger-Keldysh Closed-Time-Path formalism with two time axes and a doubling of degrees of freedom. The central structural feature of such effective actions is the coupling between degrees of freedom on the two time axes. This reflects the fact that from an effective field theory point of view, dissipation is the loss of energy of the low-energy hydrodynamical degrees of freedom to the integrated-out, UV degrees of freedom of the environment. The dynamics of only the hydrodynamical modes may therefore not posses a conserved stress-energy tensor. After a general discussion of the CTP effective actions, we use the variational principle to derive the energy-momentum balance equation for a dissipative fluid from an effective Goldstone action of the long-range hydrodynamical modes. Despite the absence of conserved energy and momentum, we show that we can construct the first-order dissipative stress-energy tensor and derive the Navier-Stokes equations near hydrodynamical equilibrium. The shear viscosity is shown to vanish in the classical theory under consideration, while the bulk viscosity is determined by the form of the effective action. We also discuss the thermodynamics of the system and analyse the entropy production.

hep-th↗

arXiv2014

Searching for Fermi Surfaces in Super-QED

The exploration of strongly-interacting finite-density states of matter has been a major recent application of gauge-gravity duality. When the theories involved have a known Lagrangian description, they are typically deformations of large $N$ supersymmetric gauge theories, which are unusual from a condensed-matter point of view. In order to better interpret the strong-coupling results from holography, an understanding of the weak-coupling behavior of such gauge theories would be useful for comparison. We take a first step in this direction by studying several simple supersymmetric and non-supersymmetric toy model gauge theories at zero temperature. Our supersymmetric examples are $\mathcal{N}=1$ super-QED and $\mathcal{N}=2$ super-QED, with finite densities of electron number and R-charge respectively. Despite the fact that fermionic fields couple to the chemical potentials we introduce, the structure of the interaction terms is such that in both of the supersymmetric cases the fermions do not develop a Fermi surface. One might suspect that all of the charge in such theories would be stored in the scalar condensates, but we show that this is not necessarily the case by giving an example of a theory without a Fermi surface where the fermions still manage to contribute to the charge density.

hep-th↗