arXiv subjects

Julian Sonner

Publications and source records attributed to Julian Sonner.

At least 55 records · Page 3Linked to original sources

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.

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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

Eigenstate thermalization in the Sachdev-Ye-Kitaev model

The eigenstate thermalization hypothesis (ETH) explains how closed unitary quantum systems can exhibit thermal behavior in pure states. In this work we examine a recently proposed microscopic model of a black hole in AdS$_2$, the so-called Sachdev-Ye-Kitaev (SYK) model. We show that this model satisfies the eigenstate thermalization hypothesis by solving the system in exact diagonalization. Using these results we also study the behavior, in eigenstates, of various measures of thermalization and scrambling of information. We establish that two-point functions in finite-energy eigenstates approximate closely their thermal counterparts and that information is scrambled in individual eigenstates. We study both the eigenstates of a single random realization of the model, as well as the model obtained after averaging of the random disordered couplings. We use our results to comment on the implications for thermal states of the dual theory, i.e. the AdS$_2$ black hole.

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arXiv2017

Decay of a Thermofield-Double State in Chaotic Quantum Systems

Scrambling in interacting quantum systems out of equilibrium is particularly effective in the chaotic regime. Under time evolution, initially localized information is said to be scrambled as it spreads throughout the entire system. This spreading can be analyzed with the spectral form factor, which is defined in terms of the analytic continuation of the partition function. The latter is equivalent to the survival probability of a thermofield double state under unitary dynamics. Using random matrices from the Gaussian unitary ensemble (GUE) as Hamiltonians for the time evolution, we obtain exact analytical expressions at finite $N$ for the survival probability. Numerical simulations of the survival probability with matrices taken from the Gaussian orthogonal ensemble (GOE) are also provided. The GOE is more suitable for our comparison with numerical results obtained with a disordered spin chain with local interactions. Common features between the random matrix and the realistic disordered model in the chaotic regime are identified. The differences that emerge as the spin model approaches a many-body localized phase are also discussed.

cond-mat.str-el↗

arXiv2017

From Conformal Blocks to Path Integrals in the Vaidya Geometry

Correlators in conformal field theory are naturally organized as a sum over conformal blocks. In holographic theories, this sum must reorganize into a path integral over bulk fields and geometries. We explore how these two sums are related in the case of a point particle moving in the background of a 3d collapsing black hole. The conformal block expansion is recast as a sum over paths of the first-quantized particle moving in the bulk geometry. Off-shell worldlines of the particle correspond to subdominant contributions in the Euclidean conformal block expansion, but these same operators must be included in order to correctly reproduce complex saddles in the Lorentzian theory. During thermalization, a complex saddle dominates under certain circumstances; in this case, the CFT correlator is not given by the Virasoro identity block in any channel, but can be recovered by summing heavy operators. This effectively converts the conformal block expansion in CFT from a sum over intermediate states to a sum over channels that mimics the bulk path integral.

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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

Black Hole Collapse in the 1/c Expansion

We present a first-principles CFT calculation corresponding to the spherical collapse of a shell of matter in three dimensional quantum gravity. In field theory terms, we describe the equilibration process, from early times to thermalization, of a CFT following a sudden injection of energy at time t=0. By formulating a continuum version of Zamolodchikov's monodromy method to calculate conformal blocks at large central charge c, we give a framework to compute a general class of probe observables in the collapse state, incorporating the full backreaction of matter fields on the dual geometry. This is illustrated by calculating a scalar field two-point function at time-like separation and the time-dependent entanglement entropy of an interval, both showing thermalization at late times. The results are in perfect agreement with previous gravity calculations in the AdS$_3$-Vaidya geometry. Information loss appears in the CFT as an explicit violation of unitarity in the 1/c expansion, restored by nonperturbative corrections.

hep-th↗

arXiv2015

Universal far-from-equilibrium Dynamics of a Holographic Superconductor

Symmetry breaking phase transitions are an example of non-equilibrium processes that require real time treatment, a major challenge in strongly coupled systems without long-lived quasiparticles. Holographic duality provides such an approach by mapping strongly coupled field theories in D dimensions into weakly coupled quantum gravity in D+1 anti-de Sitter spacetime. Here, we use holographic duality to study formation of topological defects -- winding numbers -- in the course of a superconducting transition in a strongly coupled theory in a 1D ring. When the system undergoes the transition on a given quench time, the condensate builds up with a delay that can be deduced using the Kibble-Zurek mechanism from the quench time and the universality class of the theory, as determined from the quasinormal mode spectrum of the dual model. Typical winding numbers deposited in the ring exhibit a universal fractional power law dependence on the quench time, also predicted by the Kibble-Zurek Mechanism.

hep-th↗

arXiv2014

Super-Rényi Entropy & Wilson Loops for N=4 SYM and their Gravity Duals

We compute the supersymmetric Rényi entropies across a spherical entanglement surface in N=4 SU(N) SYM theory using localization on the four-dimensional ellipsoid. We extract the leading result at large N and λ, and match its universal part to a gravity calculation involving a hyperbolically sliced supersymmetric black hole solution of N=4+ SU(2) X U(1) gauged supergravity in five dimensions. We repeat the analysis in the presence of a Wilson loop insertion and find again a perfect match with the dual string theory. Understanding the Wilson loop operator requires knowledge of the full ten-dimensional IIB supergravity solution which we elaborate upon.

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arXiv2014

Wormholes and entanglement in holography

In this essay, we consider highly entangled states in theories with a gravity dual, where the entangled degrees of freedom are causally disconnected from each other. Using the basic rules of holography, we argue that there is a non-traversable wormhole in the gravity dual whose geometry encodes the pattern of the entanglement.

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arXiv2013

Holographic Schwinger Effect and the Geometry of Entanglement

In this note we point out that the recently proposed bulk dual of an entangled pair of a quark and an anti-quark corresponds to the Lorentzian continuation of the tunneling instanton describing Schwinger pair creation in the dual field theory. This observation supports and further explains the claim by Jensen & Karch that the bulk dual of an EPR pair is a string with a wormhole on its world sheet. We suggest that this constitutes an AdS/CFT realization of the creation of a Wheeler wormhole.

hep-th↗

arXiv2013

On universality of charge transport in AdS/CFT

We develop the holographic formulation of transport in strongly coupled two-layer systems. We identify a dc conductivity, sigma^dc, that is finite even in a translationally invariant setup, and universal for CFTs with a gravity dual. The thermoelectric conductivity and heat conductivity are fully determined by the electrical conductivity matrix, as a consequence of Ward identities. We use the memory-matrix approach for double-layer systems, together with Ward identities, to show that sigma^dc - extended to finite frequency - has no Drude peak and, similarly, that its universal value is unaffected if translation invariance is softly broken.

hep-th↗

arXiv2013

Bosonic Fractionalisation Transitions

At finite density, charge in holographic systems can be sourced either by explicit matter sources in the bulk or by bulk horizons. In this paper we find bosonic solutions of both types, breaking a global U(1) symmetry in the former case and leaving it unbroken in the latter. Using a minimal bottom-up model we exhibit phase transitions between the two cases, under the influence of a relevant operator in the dual field theory. We also embed solutions and transitions of this type in M-theory, where, holding the theory at constant chemical potential, the cohesive phase is connected to a neutral phase of Schrödinger type via a z=2 QCP.

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arXiv2013

Holographic Superfluids and the Dynamics of Symmetry Breaking

We explore the far from equilibrium response of a holographic superfluid using the AdS/CFT correspondence. We establish the dynamical phase diagram corresponding to quantum quenches of the order parameter source field. We find three distinct regimes of behaviour that are related to the spectrum of black hole quasi-normal modes. These correspond to damped oscillations of the order parameter, and over-damped approaches to the superfluid and normal states. The presence of three regimes, which includes an emergent dynamical temperature scale, is argued to occur more generally in time-reversal invariant systems that display continuous symmetry breaking.

hep-th↗

arXiv2012

Competing orders in M-theory: superfluids, stripes and metamagnetism

We analyse the infinite class of d=3 CFTs dual to skew-whiffed AdS_4 X SE_7 solutions of D=11 supergravity at finite temperature and charge density and in the presence of a magnetic field. We construct black hole solutions corresponding to the unbroken phase, and at zero temperature some of these become dyonic domain walls of an Einstein-Maxwell-pseudo-scalar theory interpolating between AdS_4 in the UV and new families of dyonic AdS_2 X R^2 solutions in the IR. The black holes exhibit both diamagnetic and paramagnetic behaviour. We analyse superfluid and striped instabilities and show that for large enough values of the magnetic field the superfluid instability disappears while the striped instability remains. For larger values of the magnetic field there is also a first-order metamagnetic phase transition and at zero temperature these black hole solutions exhibit hyperscaling violation in the IR with dynamical exponent z=3/2 and θ=-2.

hep-th↗

arXiv2012

Hawking Radiation and Non-equilibrium Quantum Critical Current Noise

The dynamical scaling of quantum critical systems in thermal equilibrium may be inherited in the driven steady-state, leading to universal out-of-equilibrium behaviour. This attractive notion has been demonstrated in just a few cases. We demonstrate how holography - a mapping between the quantum critical system and a gravity dual - provides an illuminating perspective and new results. Non-trivial out-of-equilibrium universality is particularly apparent in current noise, which is dual to Hawking radiation in the gravitational system. We calculate this in a 2-dimensional system driven by a strong in-plane electric field and deduce a universal scaling function interpolating between previously established equilibrium and far-from-equilibrium current noise. Since this applies at all fields, out-of-equilibrium experiments no longer require very high fields for comparison with theory.

cond-mat.str-el↗

arXiv2011

Spectral function of the supersymmetry current

We continue our study of the retarded Green's function of the universal fermionic supersymmetry current ("supercurrent") for the most general class of d=3 N=2 SCFTs with D=10 or D=11 supergravity duals by studying the propagation of the Dirac gravitino in the electrically charged AdS-Reissner-Nordström black-brane background of N=2 minimal gauged supergravity in D=4. We expand upon results presented in a companion paper, including the absence of a Fermi surface and the appearance of a soft power-law gap at zero temperature. We also present the analytic solution of the gravitino equation in the AdS_2 X R^2 background which arises as the near-horizon limit at zero temperature. In addition we determine the quasinormal mode spectrum.

hep-th↗

arXiv2011

Universal fermionic spectral functions from string theory

We carry out the first holographic calculation of a fermionic response function for a strongly coupled $d=3$ system with an explicit D=10 or D=11 supergravity dual. By considering the supersymmetry current, we obtain a universal result applicable to all d=3 N=2 SCFTs with such duals. Surprisingly, the spectral function does not exhibit a Fermi surface, despite the fact that the system is at finite charge density. We show that it has a phonino pole and at low frequencies there is a depletion of spectral weight with a power-law scaling which is governed by a locally quantum critical point.

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