arXiv subjects

Benjamin Withers

Publications and source records attributed to Benjamin Withers.

At least 37 records · Page 2Linked to original sources

arXiv2022

Convergence of the Fefferman-Graham expansion and complex black hole anatomy

Given a set of sources and one-point function data for a Lorentzian holographic QFT, does the Fefferman-Graham expansion converge? If it does, what sets the radius of convergence, and how much of the interior of the spacetime can be reconstructed using this expansion? As a step towards answering these questions we consider real analytic CFT data, where in the absence of logarithms, the radius is set by singularities of the complex metric reached by analytically continuing the Fefferman-Graham radial coordinate. With the conformal boundary at the origin of the complex radial plane, real Lorentzian submanifolds appear as piecewise paths built from radial rays and arcs of circles centred on the origin. This allows singularities of Fefferman-Graham metric functions to be identified with gauge-invariant singularities of maximally extended black hole spacetimes, thereby clarifying the physical cause of the limited radius of convergence in such cases. We find black holes with spacelike singularities can give a radius of convergence equal to the horizon radius, however for black holes with timelike singularities the radius is smaller. We prove that a finite radius of convergence does not necessarily follow from the existence of an event horizon, a spacetime singularity, nor from caustics of the Fefferman-Graham gauge, by providing explicit examples of spacetimes with an infinite radius of convergence which contain such features.

hep-th↗

arXiv2022

Massive holographic QFTs in de Sitter

We study strongly coupled mass-deformed-CFT on a fixed de Sitter spacetime in three dimensions via holography. We elucidate the global causal structure of the four-dimensional spacetime dual to the de Sitter invariant vacuum state. The conformal boundaries of de Sitter appear as spacelike defects sourced by the mass deformation, which extend into the bulk as curvature singularities in AdS. We compute all one- and two-point functions of the deformed-CFT stress tensor and a scalar operator order-by-order in the mass deformation for a simple holographic model. These correlation functions admit a spectral representation as a sum of simple poles corresponding to normalisable modes in the bulk.

hep-th↗

arXiv2022

Hydrodynamic Gradient Expansion Diverges beyond Bjorken Flow

The gradient expansion is the fundamental organising principle underlying relativistic hydrodynamics, yet understanding its convergence properties for general nonlinear flows has posed a major challenge. We introduce a simple method to address this question in a class of fluids modelled by Israel-Stewart--type relaxation equations. We apply it to (1+1)-dimensional flows and provide numerical evidence for factorially divergent gradient expansions. This generalises results previously only obtained for (0+1)-dimensional comoving flows, notably Bjorken flow. We also demonstrate that the only known nontrivial case of a convergent hydrodynamic gradient expansion at the nonlinear level relies on Bjorken flow symmetries and becomes factorially divergent as soon as these are relaxed. Finally, we show that factorial divergence can be removed using a momentum space cutoff, which generalises a result obtained earlier in the context of linear response.

hep-th↗

arXiv2021

Hydrodynamic gradient expansion in linear response theory

A foundational question in relativistic fluid mechanics concerns the properties of the hydrodynamic gradient expansion at large orders. We establish the precise conditions under which this gradient expansion diverges for a broad class of microscopic theories admitting a relativistic hydrodynamic limit, in the linear regime. Our result does not rely on highly symmetric fluid flows utilized by previous studies of heavy-ion collisions and cosmology. The hydrodynamic gradient expansion diverges whenever energy density or velocity fields have support in momentum space exceeding a critical momentum, and converges otherwise. This critical momentum is an intrinsic property of the microscopic theory and is set by branch point singularities of hydrodynamic dispersion relations.

hep-th↗

arXiv2021

Convergence of hydrodynamic modes: insights from kinetic theory and holography

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 generally, we examine the consequences of the Implicit Function Theorem in hydrodynamics and give a prescription to determine a set of points that necessarily includes all complex singularities of the dispersion relation. This may be used as a practical tool to assist in determining the radius of convergence of hydrodynamic dispersion relations.

hep-th↗

arXiv2021

Transseries for causal diffusive systems

The large proper-time behaviour of expanding boost-invariant fluids has provided many crucial insights into quark-gluon plasma dynamics. Here we formulate and explore the late-time behaviour of nonequilibrium dynamics at the level of linearized perturbations of equilibrium, but without any special symmetry assumptions. We introduce a useful quantitative approximation scheme in which hydrodynamic modes appear as perturbative contributions while transients are nonperturbative. In this way, solutions are naturally organized into transseries as they are in the case of boost-invariant flows. We focus our attention on the ubiquitous telegrapher's equation, the simplest example of a causal theory with a hydrodynamic sector. In position space we uncover novel transient contributions as well as Stokes phenomena which change the structure of the transseries based on the spacetime region or the choice of initial data.

hep-th↗

arXiv2020

From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT

A common method to prepare states in AdS/CFT is to perform the Euclidean path integral with sources turned on for single-trace operators. These states can be interpreted as coherent states of the bulk quantum theory associated to Lorentzian initial data on a Cauchy slice. In this paper, we discuss the extent to which arbitrary initial data can be obtained in this way. We show that the initial data must be analytic and define the subset of it that can be prepared by imposing bulk regularity. Turning this around, we show that for generic analytic initial data the corresponding Euclidean section contains singularities coming from delta function sources in the bulk. We propose an interpretation of these singularities as non-perturbative objects in the microscopic theory.

hep-th↗

arXiv2019

Driven black holes: from Kolmogorov scaling to turbulent wakes

General relativity governs the nonlinear dynamics of spacetime, including black holes and their event horizons. We demonstrate that forced black hole horizons exhibit statistically steady turbulent spacetime dynamics consistent with Kolmogorov's theory of 1941. As a proof of principle we focus on black holes in asymptotically anti-de Sitter spacetimes in a large number of dimensions, where greater analytic control is gained. We also demonstrate that tidal deformations of the horizon induce turbulent dynamics. When set in motion relative to the horizon a deformation develops a turbulent spacetime wake, indicating that turbulent spacetime dynamics may play a role in binary mergers and other strong-field phenomena.

hep-th↗

arXiv2019

Hydrodynamics without boosts

We construct the general first-order hydrodynamic theory invariant under time translations, the Euclidean group of spatial transformations and preserving particle number, that is with symmetry group $\mathbb{R}_t\times$ISO$(d)\times$U$(1)$. Such theories are important in a number of distinct situations, ranging from the hydrodynamics of graphene to flocking behaviour and the coarse-grained motion of self-propelled organisms. Furthermore, given the generality of this construction, we are are able to deduce special cases with higher symmetry by taking the appropriate limits. In this way we write the complete first-order theory of Lifshitz-invariant hydrodynamics. Among other results we present a class of non-dissipative first order theories which preserve parity.

hep-th↗

arXiv2018

Linear gravity from conformal symmetry

We perform a unified systematic analysis of $d+1$ dimensional, spin $\ell$ representations of the isometry algebra of the maximally symmetric spacetimes AdS$_{d+1}$, $\mathbb{R}_{1,d}$ and dS$_{d+1}$. This allows us to explicitly construct the effective low-energy bulk equations of motion obeyed by linear fields, as the eigenvalue equation for the quadratic Casimir differential operator. We show that the bulk description of a conformal family is given by the Fierz-Pauli system of equations. For $\ell = 2$ this is a massive gravity theory, while for $\ell = 2$ conserved currents we obtain Einstein gravity and covariant gauge fixing conditions. This analysis provides a direct algebraic derivation of the familiar AdS holographic dictionary at low energies, with analogous results for Minkowski and de Sitter spacetimes.

hep-th↗

arXiv2018

Large D holography with metric deformations

We consider Einstein gravity in AdS in the presence of a deformed conformal boundary metric, in the limit of large spacetime dimension. At leading order we find a new set of effective near-horizon equations. These can be understood as covariant generalisations of the undeformed equations with new source terms due to the curvature. We show that these equations are given by the conservation of the exact second-order Landau-frame hydrodynamic stress tensor. No derivative expansions are invoked in this identification. We use the new equations to study CFTs with 2d lattice deformations, computing their quasi-normal mode spectra and thermal conductivities, both numerically and analytically to quartic order in small lattice amplitude. Many of our results also apply to asymptotically flat spacetimes.

hep-th↗

arXiv2018

Overcoming obstacles in nonequilibrium holography

We study universal spatial features of certain non-equilibrium steady states corresponding to flows of strongly correlated fluids over obstacles. This allows us to predict universal spatial features of far-from-equilibrium systems, which in certain interesting cases depend cleanly on the hydrodynamic transport coefficients of the underlying theory, such as $η/s$, the shear viscosity to entropy density ratio. In this work we give a purely field-theoretical definition of the spatial collective modes identified earlier and proceed to demonstrate their usefulness in a set of examples, drawing on hydrodynamic theory as well as holographic duality. We extend our earlier treatment by adding a finite chemical potential, which introduces a qualitatively new feature, namely damped oscillatory behavior in space. We find interesting transitions between oscillatory and damped regimes and we consider critical exponents associated with these. We explain in detail the numerical method and add a host of new examples, including fully analytical ones. Such a treatment is possible in the large-dimension limit of the bulk theory, as well as in three dimensions, where we also exhibit a fully analytic non-linear example that beautifully illustrates the original proposal of spatial universality. This allows us to explicitly demonstrate how an infinite tower of discrete modes condenses into a branch cut in the zero-temperature limit, converting exponential decay into a power law tail.

hep-th↗

arXiv2018

Short-lived modes from hydrodynamic dispersion relations

We consider the dispersion relation of the shear-diffusion mode in relativistic hydrodynamics, which we generate to high order as a series in spatial momentum q for a holographic model. We demonstrate that the hydrodynamic series can be summed in a way that extends through branch cuts present in the complex q plane, resulting in the accurate description of multiple sheets. Each additional sheet corresponds to the dispersion relation of a different non-hydrodynamic mode. As an example we extract the frequencies of a pair of oscillatory non-hydrodynamic black hole quasinormal modes from the hydrodynamic series. The analytic structure of this model points to the possibility that the complete spectrum of gravitational quasinormal modes may be accessible from the hydrodynamic derivative expansion.

hep-th↗

arXiv2017

Universal spatial structure of nonequilibrium steady states

We describe a large family of nonequilibrium steady states (NESS) corresponding to forced flows over obstacles. The spatial structure at large distances from the obstacle is shown to be universal, and can be quantitatively characterised in terms of certain collective modes of the strongly coupled many body system, which we define in this work. In holography, these modes are spatial analogues of quasinormal modes, which are known to be responsible for universal aspects of relaxation of time dependent systems. These modes can be both hydrodynamical or non-hydrodynamical in origin. The decay lengths of the hydrodynamic modes are set by $η/s$, the shear viscosity over entropy density ratio, suggesting a new route to experimentally measuring this ratio. We also point out a new class of nonequilibrium phase transitions, across which the spatial structure of the NESS undergoes a dramatic change, characterised by the properties of the spectrum of these spatial collective modes.

hep-th↗

arXiv2017

Robinson-Trautman spacetimes and gauge/gravity duality

We study far-from-equilibrium field theory dynamics using gauge/gravity duality applied to the Robinson-Trautman (RT) class of spacetimes and we present a number of new results. First, we assess the applicability of the hydrodynamic approximation to inhomogeneous plasma dynamics dual to RT spacetimes. We prove that to any order in a late time expansion it is possible to identify variables corresponding to the local energy density and fluid velocity. However, we show using numerical examples that this does not hold at the non-perturbative level; for sufficiently inhomogeneous initial data a local rest frame does not exist. Second, we preset a new class of holographic inhomogeneous plasma flows on the plane. The corresponding spacetimes are not of the RT type but they can be obtained from RT spacetimes with spatially compact boundaries by coordinate transformations which generate Poincaré patch-like coordinates with planar boundaries. We demonstrate the application of this procedure using numerical examples.

hep-th↗

arXiv2016

Nonlinear conductivity and the ringdown of currents in metallic holography

We study the electric and heat current response resulting from an electric field quench in a holographic model of momentum relaxation at nonzero charge density. After turning the electric field off, currents return to equilibrium as governed by the vector quasi-normal modes of the dual black brane, whose spectrum depends qualitatively on a parameter controlling the strength of inhomogeneity. We explore the dynamical phase diagram as a function of this parameter, showing that signatures of incoherent transport become identifiable as an oscillatory ringdown of the heat current. We also study nonlinear conductivity by holding the electric field constant. For small electric fields a balance is reached between the driving electric field and the momentum sink -- a steady state described by DC linear response. For large electric fields Joule heating becomes important and the black branes exhibit significant time dependence. In a regime where the rate of temperature increase is small, the nonlinear electrical conductivity is well approximated by the DC linear response calculation at an appropriate effective temperature.

hep-th↗

arXiv2016

Self-similar equilibration of strongly interacting systems from holography

We study the equilibration of a class of far-from-equilibrium strongly interacting systems using gauge/gravity duality. The systems we analyse are 2+1 dimensional and have a four dimensional gravitational dual. A prototype example of a system we analyse is the equilibration of a two dimensional fluid which is translational invariant in one direction and is attached to two different heat baths with different temperatures at infinity in the other direction. We realise such setup in gauge/gravity duality by joining two semi-infinite asymptotically Anti-de Sitter (AdS) black branes of different temperatures, which subsequently evolve towards equilibrium by emitting gravitational radiation towards the boundary of AdS. At sufficiently late times the solution converges to a similarity solution, which is only sensitive to the left and right equilibrium states and not to the details of the initial conditions. This attractor solution not only incorporates the growing region of equilibrated plasma but also the outwardly-propagating transition regions, and can be constructed by solving a single ordinary differential equation.

hep-th↗

arXiv2015

Drude in D major

We study holographic momentum relaxation in the limit of a large number of spacetime dimensions D. For an axion model we find that momentum conservation is restored as D becomes large. To compensate we scale the strength of the sources with D so that momentum is relaxed even at infinite D. We analytically obtain the quasi-normal modes which control electric and heat transport, and give their frequencies in a 1/D expansion. We also obtain the AC thermal conductivity as an expansion in 1/D, which at leading order takes Drude form. To order 1/D our analytical result provides a reasonable approximation to the AC conductivity even at D=4, establishing large D as a practical method in this context. As a further application, we discuss the signature of the transition from coherent to incoherent behaviour known to exist in the system for finite D.

hep-th↗