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We study the out-of-equilibrium dynamics induced by a local perturbation in fracton field theory. For the ${\mathbb Z}_4$ and ${\mathbb Z}_8$-symmetric free fractonic theories, we compute the time dynamics of several observables such as the two-point Green function, $\langle \phi^2 \rangle$ condensate, energy density, and the dipole momentum. The time-dependent considerations highlight that the free fractonic theory breaks causality and exhibits instantaneous signal propagation, even if an additional relativistic term is included to enforce a speed limit in the system. We show that it is related to the fact that the Lieb-Robinson bound does not hold in the continuum limit of the fracton field theory, and the effective bounded speed of light does not emerge. For the theory in finite volume, we show that the fracton wave front acquires fractal shape with non-trivial Hausdorff dimension, and argue that this phenomenon cannot be explained by a simple self-interference effect., Comment: v1: 25 pages, 7 figures; v2: 25 pages, 7 figures, references added, minor corrections; v3: 32 pages, 8 figures, chapter 5 added; v4: 32 pages, 8 figures, acknowledgments updated

We study out-of-equilibrium dynamics caused by global quantum quenches in fractonic scalar field theories. We consider several types of quenches, in particular, the mass quench in theories with different types of discrete rotational symmetries ($\mathbb{Z}_4$ and $\mathbb{Z}_8$), as well as an instantaneous quench via the transition between them. We also investigate fractonic boundary quenches, where the initial state is prepared on a finite-width slab in Euclidean time. We find that perturbing a fractonic system in finite volume especially highlights the restricted mobility via the formation and subsequent evolution of specific $\mathbb{Z}_4$-symmetric spatial structures. We discuss a generalization to $\mathbb{Z}_n$-symmetric field theories, and introduce a proper regularization, which allows us to explicitly deal with divergences inherent to fractonic field theories., Comment: v1: 21 pages, 8 figures; v2: 20 pages, 8 figures, minor corrections; v3: 21 pages, 9 figures, minor corrections

In this paper, we investigate topological modes of different physical systems defined on arbitrary two-dimensional curved surfaces. We consider the shallow water equations, inhomogeneous Maxwell's equations, Jackiw-Rebbi model and show how the topological protection mechanism responses to the presence of curvature in different situations. We show the existence of a line gap in the considered models and study the condition on the curve which can host topological modes., Comment: v1:20 pages; v2: 24 pages, results are generalized, presentation improved

In this paper, we study the holographic quantum error correcting code properties in different boundary fractal-like structures. We construct and explore different examples of the uberholographic bulk reconstruction corresponding to these structures in higher dimensions for Cantor-like sets, thermal states and $T\overline{T}$-deformed conformal field theories. We show how the growth of the system dimension emphasizes the role of the Cantor set, due to the special bound naturally arising in this context., Comment: v1: 13 pages, 4 figures; v2: references added, typos corrected

In this paper, we study entanglement islands and the Page curve in the eternal four-dimensional Schwarzschild black hole surrounded by finite temperature conformal matter. By finite temperature conformal matter we mean the matter described by the thermal density matrix, rather than the usually considered matter above the Fock vacuum. We take the matter and the black hole at different temperatures and calculate the entanglement entropy for such a setup using the s-wave approximation. As a result, we obtain that at late times the island prescription leads to the exponential growth of the entanglement entropy of conformal matter in thermal vacuum., Comment: 14 pages, 2 figures

In this paper, we initiate the study of operator local quenches in non-conformal field theories. We consider the dynamics of excited local states in massive scalar field theory in an arbitrary spacetime dimension and generalize the well-known two-dimensional CFT results. We derive the energy density, $U(1)$-charge density and $\phi^2(x)$-condensate post-quench dynamics, and identify different regimes of their evolution depending on the values of the field mass and the quench regularization parameter. For local quenches in higher-dimensional free massless scalar theories, we reproduce the structure of the available holographic results. We also investigate the local quenches in massive scalar field theory on a cylinder and show that they cause an erratic and chaotic-like evolution of observables with a complicated localization/delocalization pattern., Comment: v1: 46 pages, 13 figures; v2: 46 pages, 13 figures, references added, typos corrected; v3: 48 pages, 16 figures, details added, references added, typos corrected

In this paper, we study the fine structure of entanglement in holographic two-dimensional boundary conformal field theories (BCFT) in terms of the spatially resolved quasilocal extension of entanglement entropy - entanglement contour. We find that the boundary induces discontinuities in the contour revealing hidden localization-delocalization patterns of entanglement degrees of freedom. Moreover, we observe the formation of ``islands'' where the entanglement contour vanishes identically implying that these regions do not contribute to the entanglement at all. We argue that these phenomena are the manifestation of entanglement islands discussed recently in the literature. We apply the entanglement contour proposal to the recently proposed BCFT black hole models reproducing the Page curve - moving mirror model and the pair of BCFT in the thermofield double state. From the viewpoint of entanglement contour, the Page curve also carries the imprint of strong delocalization caused by dynamical entanglement islands., Comment: 19 pages, 6 figures

In this note, we consider the question of classicality for the theory which is known to be the effective description of two-dimensional black holes - the Morse quantum mechanics. We calculate the Wigner function and the Fisher information characterizing classicality/quantumness of single-particle systems and briefly discuss further directions to study., Comment: 15 pages, 4 figures

In this Letter, we bring together two topics in the holographic correspondence - quantum chaos and quark-gluon plasma (QGP). We establish that the first relativistic correction to drag force experienced by a charge carrier moving through a thermal medium (for example, a quark in QGP) at a constant velocity is fixed by the butterfly velocity. Moreover, we show that this result is robust against stringy corrections and anisotropy. For the jet quenching parameter, we find that it is related to the butterfly velocity along the momentum broadening direction and temperature in the spirit of the ``Planckian bound''. This opens a way to the reconstruction of butterfly velocity of quark-gluon plasma and other strongly-coupled systems experimentally from rather simple observables., Comment: v2: 11 pages

In this note, we study the holographic CFT in the de Sitter static patch at finite temperature $T$ and chemical potential. We find that butterfly velocity $v_B$ in such field theory degenerates for all values of the Hubble parameter $H$ and $T$. We interpret this as a chaos disruption caused by the interplay between the expansion of chaotic correlations constrained by $v_B$ and effects caused by de Sitter curvature. The chemical potential restores healthy butterfly velocity for some range of temperatures. Also, we provide some analogy of this chaos suppression with the Schwinger effect in de Sitter and black hole formation from shock wave collision., Comment: v1: 9 pages, v2: 15 pages, 2 figures

In this paper, we study 2d Floquet conformal field theory, where the external periodic driving is described by iterated logistic or tent maps. These maps are known to be typical examples of dynamical systems exhibiting the order-chaos transition, and we show that, as a result of such driving, the entanglement entropy scaling develops fractal features when the corresponding dynamical system approaches the chaotic regime. For the driving set by the logistic map, fractal contribution to the scaling dominates, making entanglement entropy highly oscillating function of the subsystem size., Comment: v5: affiliations added v4: 13 pages (including Supplemental Material), 19 figures, analysis of the Hausdorff dimensions added, SM extended; see also 2006.10054 and 2006.10072 for fractals in 2d Floquet CFT

In this paper, we study $\lambda \phi^4$ scalar field theory defined on the unramified extension of p-adic numbers ${\mathbb Q}_{p^n}$. For different ``space-time'' dimensions $n$, we compute one-loop quantum corrections to the effective potential. Surprisingly, despite the unusual properties of non-Archimedean geometry, the Coleman-Weinberg potential of p-adic field theory has a structure very similar to that of its real cousin. We also study two formal limits of the effective potential, $p \rightarrow 1$ and $p \rightarrow \infty$. We show that the $p\rightarrow 1$ limit allows to reconstruct the canonical result for real field theory from the p-adic effective potential and provide an explanation of this fact. On the other hand, in the $p\rightarrow\infty$ limit, the theory exhibits very peculiar behavior with emerging logarithmic terms in the effective potential, which has no analog in real theories., Comment: 23 pages, no figures; comments are welcome

We propose a charged falling particle in an AdS space as a holographic model of local charged quench generalizing model of arXiv:1302.5703. The quench is followed by evolving currents and inhomogeneous distribution of chemical potential. We derive the analytical formula describing the evolution of the entanglement entropy. At some characteristic time after the quench, we find that the entanglement shows a sharp dip. This effect is universal and independent of the dimension of the system. At finite temperature generalization of this model, we find that multiple dips and ramps appear., Comment: 22 pages, 8 figures; v3: 24 pages, 9 figures

In this paper, we study the entanglement contour in a general excited state in the holographic 2d CFT using the partial entanglement entropy proposal. We show how thermodynamics fixes the entanglement contour relating it to the first law of entanglement. We derive the entanglement contour for a general time-dependent excited state and consider a quenched initial state in the presence of spatial boundaries as an explicit example. Finally, we comment on the coarse-graining and the complexity contour in the $AdS_3/CFT_2$., Comment: 17 pages, 1 fig; v2: 21 pages, 3 figs, references added, v3: final version, the title is slightly changed

This paper is devoted to the study of the evolution of holographic complexity after a local perturbation of the system at finite temperature. We calculate the complexity using both the complexity=action(CA) and the complexity=volume(CA) conjectures and find that the CV complexity of the total state shows the unbounded late time linear growth. The CA computation shows linear growth with fast saturation to a constant value. We estimate the CV and CA complexity linear growth coefficients and show, that finite temperature leads to violation of the Lloyd bound for CA complexity. Also it is shown that for composite system after the local quench the state with minimal entanglement may correspond to the maximal complexity., Comment: 17 pp., 5 figs; v2:ref. added, minor corrections

This is the contribution to Quarks'2018 conference proceedings. This contribution is devoted to the holographic description of chaos and quantum complexity in the strongly interacting systems out of equilibrium. In the first part of the talk we present different holographic complexity proposals in out-of-equilibrium CFT following the local perturbation. The second part is devoted to the chaotic growth of the local operator size at a finite chemical potential. There are numerous results stating that the chemical potential may lead to the chaos disappearance, and we confirm these results from holographic viewpoint., Comment: 8 pp., 5 figures

This note is devoted to the investigation of Susskind's proposal(arXiv:1802.01198) concerning the correspondence between the operator growth in chaotic theories and the radial momenta of the particle falling in the AdS black hole. We study this proposal and consider the simple example of an operator with the global charge described by the charged particle falling to the Reissner-Nordstrom-AdS black hole. Different charges of the particle lead to qualitatively different behavior of the particle momenta and consequently change of the operator size behavior. This holographic result is supported by different examples of chaotic models at a finite chemical potential where the suppression of chaos has been observed., Comment: v1: 7 pages, 2 figures; v2: formula 3.4 is corrected; v3: discussion is enlarged; v4: new chapter, v5: published version

We study the evolution of holographic complexity of pure and mixed states in $1+1$-dimensional conformal field theory following a local quench using both the "complexity equals volume" (CV) and the "complexity equals action" (CA) conjectures. We compare the complexity evolution to the evolution of entanglement entropy and entanglement density, discuss the Lloyd computational bound and demonstrate its saturation in certain regimes. We argue that the conjectured holographic complexities exhibit some non-trivial features indicating that they capture important properties of what is expected to be effective (or physical) complexity., Comment: 33 pages, 19 figures; v2: typos corrected; 35 pages, references added, new appendix. Version to match published in JHEP

In this paper, we study behaviour of Wilson loops in the boost-invariant nonequilibrium anisotropic quark-gluon plasma produced in heavy-ion collisions within the holographic approach. We describe the thermalization studying the evolution of the Vaidya metric in the boost-invariant and spatially anisotropic background. To probe the system during this process we calculate rectangular Wilson loops oriented in different spatial directions. We find that anisotropic effects are more visible for the Wilson loops lying in the transversal plane unlike the Wilson loops with partially longitudinal orientation. In particular, we observe that the Wilson loops can thermalizes first unlike to the order of the isotropic model. We see that Wilson loops on transversal contours have the shortest thermalization time. We also calculate the string tension and the pseudopotential at different temperatures for the static quark-gluon plasma. We show that the pseudopotential related to the configuration on the transversal plane has the screened Cornell form. We also show that the jet-quenching parameter related with the average of the light-like Wilson loop exhibits the dependence on orientations., Comment: 39 pages, 12 figures; v3: typos corrected, to appear in Nucl. Phys. B