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Abstract We demonstrate the turbulent dynamics of the Nambu-Goto open string in the AdS3 spacetime. While the motion of a classical closed string in AdS is known to be integrable, the integrability of an open string motion depends on the boundary conditions at the string endpoints. We numerically solve the equations of motion of the open string under the boundary conditions where the endpoints are i) fixed to a finite radial coordinate in AdS, and ii) free. For i), we find turbulence on the string, that shows a cascade in the energy and angular momentum spectra. This result indicates the non-integrability of the open string with this type of boundary conditions. For ii), we find no turbulence. This is consistent with the integrability of the open string with the free boundary conditions.

Abstract We study the origin of turbulence on the string worldsheet with boundaries laid in anti de Sitter (AdS) spacetime. While the classical motion of a single closed string in AdS is integrable, it has recently been recognized that weak turbulence arises in the case of an open string suspended from the AdS boundary. In the open string case, it is necessary to impose boundary conditions on the worldsheet boundaries. We classify which boundary conditions preserve integrability. Based on this classification, we anticipate that turbulence may occur on the string worldsheet if integrability is not guaranteed by the boundary conditions. Numerical investigations of the classical open-string dynamics support that turbulence occurs when the boundary conditions are not integrable.

Abstract Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic system, and numerically evaluate Krylov complexity for operators and states. Despite no exponential growth of the Krylov complexity, we find a clear correlation between variances of Lanczos coefficients and classical Lyapunov exponents, and also a correlation with the statistical distribution of adjacent spacings of the quantum energy levels. This shows that the variances of Lanczos coefficients can be a measure of quantum chaos. The universality of the result is supported by our similar analysis of Sinai billiards. Our work provides a firm bridge between Krylov complexity and classical/quantum chaos.

Abstract We find, in the AdS/CFT, a source on the boundary which generates one wave packet drawing a null geodesic inside the bulk. Once such a wave packet dives into the bulk, it comes back to the boundary after a specific time, at which the expectation value of the corresponding boundary operator finally stands up. Since this behavior strongly reflects the existence of the holographic spacetime, our technique will be helpful in identifying holographic materials.

Abstract We construct a cohomogeneity-1 helical black string in six-dimensional Einstein gravity. The helical solution branches from the onset of the gravitational superradiant instability of the equal-spinning Myers-Perry black string. The isometry group of the helical black string is ℝ T × U(1) Z × SU(2), where the first two are helical isometries generated by linear combinations of time translation, shifts along the string, and rotation, each of which is individually broken by the superradiant instability. The helical black string is stationary, non-axisymmetric, and has nonzero horizon velocity despite the absence of momentum in the string direction. The entropy of the helical black string is higher than that of the Myers-Perry black string, but lower than cohomogeneity-2 “black resonator strings” (recently found) when the solutions overlap in the microcanonical ensemble. The entropy of the helical black string approaches zero when the horizon velocity along the string reaches its maximum given by the speed of light. Nevertheless, we find no evidence for the existence of regular horizonless solutions in this limit.

Abstract We construct novel black strings that are neither time-translation invariant, nor axisymmetric, nor translationally invariant in the string direction, but nevertheless have a helical Killing vector field. These solutions branch from the superradiant instability of D = 6 Myers-Perry black strings with equal angular momenta. We coin these solutions as black resonator strings and we find that they have more entropy than Myers-Perry black strings for the energies and angular momenta where both solutions coexist. We also construct Kaluza-Klein geons, which share the symmetries of black resonator strings, but are horizonless. Unlike in other superradiant systems, Kaluza-Klein geons are not the horizonless limit of black resonator strings and are instead entirely separate solutions.

Abstract We investigate the effect of superradiant scattering of gravitational perturbations on the stability of rotating black strings, focusing on the six dimensional equal-spinning Myers-Perry black string. We find that rapidly rotating black strings are unstable to gravitational superradiant modes within a bounded range of string lengths. The instability occurs because momentum along the string direction creates a potential barrier that allows for the confinement of superradiant modes. Yet, five dimensional Myers-Perry black holes do not have stable particle orbits so, unlike other known superradiant systems, these black strings remain stable to perturbations with sufficiently high azimuthal mode number — this is a ‘finite-m’ superradiant instability. For some parameters, this instability competes with the Gregory-Laflamme instability, but otherwise exists independently. The onset of this instability is degenerate and branches to multiple steady-state solutions. This paper is the first of a trilogy: in the next two, we construct two distinct families of rotating strings emerging from the superradiant onset (the ‘black resonator strings’ and ‘helical black strings’). We argue that similar physics is present in 5-dimensional Kerr black strings, but not in D > 6 equal-spinning Myers-Perry black strings.

Abstract Superradiance is known as a wave amplification process caused by rotating or charged black holes. We argue that the superradiance of stationary black holes in asymptotically AdS spacetimes can be characterized by the ability of energy extraction. Specifically, we demonstrate that energy can be extracted from Reissner-Nordström-AdS4 and Kerr-AdS4 under appropriate time-dependent boundary conditions at conformal boundaries. This indicates that energy can be extracted from thermal states dual to these black holes by applying appropriate time-dependent sources. We also show that the energy extraction can be realized as a reversible process.

Abstract We propose a way to observe the photon ring of the asymptotically anti-de Sitter black hole dual to a superconductor on the two-dimensional sphere. We consider the electric current of the superconductor under the localized time-periodic external electromagnetic field. On the gravity side, the bulk Maxwell field is sent from the AdS boundary and then diffracted by the black hole. We construct the image of the black hole from the asymptotic data of the bulk Maxwell field that corresponds to the electric current on the field theory side. We decompose the electric current into the dissipative and non-dissipative parts and take the dissipative part for the imaging of the black hole. We investigate the effect of the charged scalar condensate on the image. We obtain the bulk images that indicate the discontinuous change of the size of the photon ring.

Abstract We study rotating global AdS solutions in five-dimensional Einstein gravity coupled to a multiplet complex scalar within a cohomogeneity-1 ansatz. The onset of the gravitational and scalar field superradiant instabilities of the Myers-Perry-AdS black hole mark bifurcation points to black resonators and hairy Myers-Perry-AdS black holes, respectively. These solutions are subject to the other (gravitational or scalar) instability, and result in hairy black resonators which contain both gravitational and scalar hair. The hairy black resonators have smooth zero-horizon limits that we call graviboson stars. In the hairy black resonator and graviboson solutions, multiple scalar components with different frequencies are excited, and hence these are multioscillating solutions. The phase structure of the solutions are examined in the microcanonical ensemble, i.e. at fixed energy and angular momenta. It is found that the entropy of the hairy black resonator is never the largest among them. We also find that hairy black holes with higher scalar wavenumbers are entropically dominant and occupy more of phase space than those of lower wavenumbers.

Abstract The AdS soliton is a nonsingular spacetime that has a flat conformal boundary with a compact S 1 direction. We find a horizonless cohomogeneity-1 metric that describes nonlinear gravitational oscillations of the AdS soliton in five dimensions. We call this spacetime the resonating AdS soliton. This solution is obtained as the nonlinear extension of normal modes of the AdS soliton dual to spin-2 glueball excitations. The boundary energy momentum tensor of the resonating AdS soliton has time periodic components, and it is interpreted as a coherently excited state in the dual field theory. Physical quantities of the resonating AdS soliton are multivalued at a fixed energy, suggesting a transition between different frequency solutions. The energy of the resonating AdS soliton is higher than that of the undeformed AdS soliton, in accordance with the positive energy conjecture proposed by Horowitz and Myers.

Abstract Black resonators and geons in global AdS are rapidly rotating, low-energy solutions with a helical Killing field. We study the linear mode stability of equal angular momenta, five-dimensional black resonators and geons under scalar, electromagnetic, and gravitational perturbations. We find that black resonators are unstable to the superradiant instability, in agreement with previously known results. Perhaps surprisingly, many geons appear linearly stable, despite having an ergoregion. This apparent stability implies that geons are important long-lived, low-energy states in the dual gauge theory. However, we do find that geons are unstable within a certain range of parameter space. We comment on the nature of this instability and to its possible endpoints. We also report on new non-spinning oscillating geons, which we construct within a cohomogeneity two ansatz. Given the existing arguments that suggest our linear stability results may be extended nonlinearly, our findings indicate that most geons are generic and long-lived solutions.

Abstract With the aim to reveal universal features of hadronic matter and correlated Dirac insulators in strong AC-electric fields, we study the N=2 $$ \mathcal{N}=2 $$ supersymmetric QCD with a finite quark mass driven by a rotating electric field ℰ x + iℰ y = ℰe iΩt . The analysis is done in the holographically dual D3/D7 system in the co-rotating frame, effectively. The nonequilibrium phase diagram is determined from the threshold electric field at which the insulator phase breaks down to a conductive phase due to the AC version of the Schwinger mechanism. The external field induces a rotating current Jx+iJy=JeiΩt $$ {\mathcal{J}}_x+\kern0.62em i{\mathcal{J}}_y=\mathcal{J}{e^i}^{\Omega t} $$ originating from vacuum polarization and dissipative current in the insulating and conductive phases respectively. Intriguing features are observed as the frequency Ω approaches resonance with the meson excitation energy Ωmeson. There, the threshold minimizes and a condensate of vector mesons with oscillating current exists even in the zero driving field limit. This state, which we call Floquet condensate of vector mesons, is expected to be dynamically stable realizing a non-thermal fixed point that breaks time translational and reversal symmetries. Our finding has many similarities with exciton BEC discussed in solid state systems, where the semiconductor is to be replaced by materials hosting gapped Dirac electrons, e.g. 3D topological insulators or bismuth. Vector meson Floquet condensate may also have implications in the pre-thermalized dynamics in heavy ion collision experiments.

Abstract We demonstrate that a holographic model of the Einstein-Podolsky-Rosen pair exhibits fast scrambling. Strongly entangled quark and antiquark in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory are considered. Their gravity dual is a fundamental string whose endpoints are uniformly accelerated in opposite direction. We slightly increase the acceleration of the endpoint and show that it quickly destroys the correlation between the quark and antiquark. The proper time scale of the destruction is τ ∗ ∼ β ln S where β is the inverse Unruh temperature and S is the entropy of the accelerating quark. We also evaluate the Lyapunov exponent from correlation function as λ L = 2π/β, which saturates the Lyapunov bound. Our results suggest that the fast scrambling or saturation of the Lyapunov bound do not directly imply the existence of an Einstein dual. When we slightly decrease the acceleration, the quark and antiquark are causally connected and an "one-way traversable wormhole" is created on the worldsheet. It causes the divergence of the correlation function between the quark and antiquark.

Abstract The out-of-time-order correlator (OTOC) is considered as a measure of quantum chaos. We formulate how to calculate the OTOC for quantum mechanics with a general Hamiltonian. We demonstrate explicit calculations of OTOCs for a harmonic oscillator, a particle in a one-dimensional box, a circle billiard and stadium billiards. For the first two cases, OTOCs are periodic in time because of their commensurable energy spectra. For the circle and stadium billiards, they are not recursive but saturate to constant values which are linear in temperature. Although the stadium billiard is a typical example of the classical chaos, an expected exponential growth of the OTOC is not found. We also discuss the classical limit of the OTOC. Analysis of a time evolution of a wavepacket in a box shows that the OTOC can deviate from its classical value at a time much earlier than the Ehrenfest time, which could be the reason of the difficulty for the numerical analyses to exhibit the exponential growth.

Abstract Floquet states can be realized in quantum systems driven by continuous time-periodic perturbations. It is known that a state known as the Floquet Weyl semimetal can be realized when free Dirac fermions are placed in a rotating electric field. What will happen if strong interaction is introduced to this system? Will the interaction wash out the characteristic features of Weyl semimetals such as the Hall response? Is there a steady state and what is its thermodynamic behavior? We answer these questions using AdS/CFT correspondence in the N $$ \mathcal{N} $$ = 2 supersymmetric massless QCD in a rotating electric field in the large N c limit realizing the first example of a “holographic Floquet state”. In this limit, gluons not only mediate interaction, but also act as an energy reservoir and stabilize the nonequilibrium steady state (NESS). We obtain the electric current induced by a rotating electric field: in the high frequency region, the Ohm’s law is satisfied, while we recover the DC nonlinear conductivity at low frequency, which was obtained holographically in a previous work. The thermodynamic properties of the NESS, e.g., fluctuation-dissipation relation, is characterized by the effective Hawking temperature that is defined from the effective horizon giving a holographic meaning to the “periodic thermodynamic” concept. In addition to the strong (pump) rotating electric field, we apply an additional weak (probe) electric field in the spirit of the pump-probe experiments done in condensed matter experiments. Weak DC and AC probe analysis in the background rotating electric field shows Hall currents as a linear response, therefore the Hall response of Floquet Weyl semimetals survives at the strong coupling limit. We also find frequency mixed response currents, i.e., a heterodyning effect, characteristic to periodically driven Floquet systems.

Based on the QCD string picture at confining phase, we conjecture that the deconfinement transition always accompanies a condensation of higher meson resonances with a power-law behavior, “meson turbulence”. We employ the AdS/CFT correspondence to calculate the meson turbulence for N=2 supersymmetric QCD at large Nc and at strong coupling limit, and find that the energy distribution to each meson level n scales as nα with the universal scaling α=−5. The universality is checked for various ways to attain the quark deconfinement: a static electric field below/around the critical value, a time-dependent electric field quench, and a time-dependent quark mass quench, all result in the turbulent meson condensation with the universal power α=−5 around the deconfinement.

In a QCD-like strongly coupled gauge theory at large Nc, using the AdS/CFT correspondence, we find that heavy quark deconfinement is accompanied by a coherent condensation of higher meson resonances. This is revealed in non-equilibrium deconfinement transitions triggered by static, as well as quenched electric fields even below the Schwinger limit. There, we observe a “turbulent” energy flow to higher meson modes, which finally results in the quark deconfinement. Our observation is consistent with seeing deconfinement as a condensation of long QCD strings.

Rapidly rotating Myers–Perry-AdS5 (MPAdS5) black holes are shown to be unstable against rotational superradiance of a Maxwell field. From the onset of the instability, time-periodic neutral black hole solutions equipped with a nontrivial electromagnetic wave are obtained, which we call photonic black resonators. In the horizonless limit, they reduce to geon solutions which may be called photon stars. Specifically, we introduce a cohomogeneity-1 ansatz for the metric and Maxwell field and construct such solutions with an isometry group. We compute thermodynamic quantities and obtain phase diagrams. It turns out that a photonic black resonator has a higher entropy than a MPAdS5 black hole, while it also has a smaller entropy than a black resonator without the Maxwell field. This suggests what is expected for nonlinear dynamics following the Maxwell superradiant instability with the isometry. [ABSTRACT FROM AUTHOR]

We construct dynamical black hole solutions with a helical symmetry in AdS5, called black resonators, as well as their horizonless limits, called geons. We introduce a cohomogeneity-1 metric describing a class of black resonators and geons whose isometry group is . This allows us to study them in a wide range of parameters. We obtain the phase diagram for the black resonators, geons, and Myers–Perry-AdS5, where the black resonators emerge from the onset of a superradiant instability of the Myers–Perry-AdS5 with equal angular momenta and are connected to the geons in the small horizon limit. The angular velocities of the black resonators always satisfy in units of the AdS radius. A black resonator is shown to have higher entropy than a Myers–Perry-AdS5 black hole with the same asymptotic charges. This implies that the Myers–Perry-AdS5 can dynamically evolve into the black resonator under the exact -symmetry although its endpoint will be further unstable to -violating perturbations. [ABSTRACT FROM AUTHOR]

Assigning a chaos index for dynamics of generic quantum field theories is a challenging problem because the notion of a Lyapunov exponent, which is useful for singling out chaotic behavior, works only in classical systems. We address the issue by using the AdS/CFT correspondence, as the large Nc limit provides a classicalization (other than the standard ℏ→0) while keeping nontrivial quantum condensation. We demonstrate the chaos in the dynamics of quantum gauge theories: The time evolution of homogeneous quark condensates ⟨qq⟩ and ⟨qγ5q⟩ in an N=2 supersymmetric QCD with the SU(Nc) gauge group at large Nc and at a large 't Hooft coupling λ≡NcgYM² exhibits a positive Lyapunov exponent. The chaos dominates the phase space for energy density E≳(6×10²)×mq4(Nc/λ²), where mq is the quark mass. We evaluate the largest Lyapunov exponent as a function of (Nc,λ,E) and find that the N=2 supersymmetric QCD is more chaotic for smaller Nc. [ABSTRACT FROM AUTHOR]

Clarifying conditions for the existence of a gravitational picture for a given quantum field theory (QFT) is one of the fundamental problems in the AdS/CFT correspondence. We propose a direct way to demonstrate the existence of the dual black holes: imaging an Einstein ring. We consider a response function of the thermal QFT on a two-dimensional sphere under a time-periodic localized source. The dual gravity picture, if it exists, is a black hole in an asymptotic global AdS4 and a bulk probe field with a localized source on the AdS boundary. The response function corresponds to the asymptotic data of the bulk field propagating in the black hole spacetime. We find a formula that converts the response function to the image of the dual black hole: The view of the sky of the AdS bulk from a point on the boundary. Using the formula, we demonstrate that, for a thermal state dual to the Schwarzschild-AdS4 spacetime, the Einstein ring is constructed from the response function. The evaluated Einstein radius is found to be determined by the total energy of the dual QFT. Our theoretical proposal opens a door to gravitational phenomena on strongly correlated materials. [ABSTRACT FROM AUTHOR]