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A brief sketch of the results obtained is presented. To embed the obtained results in a general framework, we start by presenting a recent status of bottom-up holographic QCD (HQCD) models’ applications to the studies of the formation and properties of quark–gluon matter. Our considerations of HQCD under conditions of high baryon densities attainable at the NICA experimental complex are presented.

We study the confinement/deconfinement phase diagram within a five-dimensional fully anisotropic holographic model supported by Einsteindilaton-three-Maxwell action. One of the Maxwell fields provides the chemical potential, the second Maxwell field represents real spacial anisotropy of the QGP produced in heavy-ion collisions and the third Maxwell field is related to an external magnetic field. Influence of the so-called primary anisotropy due to the non-centrality of the heavy-ion collision and secondary anisotropy originating from the external magnetic field on the phase diagram is considered. Based on recent work [1,2].

We consider holographic renormalization group flow equations in an anisotropic quark—gluon plasma and present anisotropic solutions for some special cases.

We investigate various aspects of AdS2 wormholes in Jackiw—Teitelboim gravity and their holographic applications. We first study the AdS2 space in global coordinates traversable by virtue of the presence of pointlike matter violating the dominant energy condition. We calculate the evolution of the entanglement entropy in such a system. We then investigate the construction proposed by Verlinde and colleagues describing states similar to wormholes. These states are called partially entangled thermal states. We propose a construction similar to the geometries of such states using conformal maps of the upper halfplane. We study correlation functions in theories dual to such geometries and also comment on the possible connection between a special type of partially entangled thermal states and violation of replica symmetry.

We briefly review recent applications of holographic renormalization group flow equations in a hot and dense quark-gluon plasma (QGP). We especially focus on presenting a few examples typically used in the holographic description of the QGP. We study the influence of the chemical potential on the holographic β-function in these examples.

We propose to relate the entanglement entropy of the three-dimensional collisions region of two ions moving towards each other with the multiplicity of particles produced in this region. We calculate holographic entanglement entropy of elongated and differently oriented relative to the beam-line three-dimensional regions, and estimate the multiplicity of particles produced in peripheral and central collisions. These qualities show significal fluctuations near the critical temperature for given chemical potential. The fluctuations themselves are strongly dependent on anisotropy and orientation.

We consider entanglement entropy quantities for a three-part system, namely, the tripartite information, total correlation, and so-called secrecy monotone. A holographic approach is used to calculate the time evolution of the entanglement entropy during nonequilibrium heating, which leads to holographic definitions of these quantities. We study time dependence of these three quantities.

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

International audience; This survey was written by students of L. D. Faddeev under the editorship of L. A. Takhtajan. Sections 1.1, 1.2, 2–4, and 6 were written by Takhtajan, §§1.3 and 1.4 by F. A. Smirnov, §§5.1 and 5.2 by E. K. Sklyanin, §§5.3–5.6 by Sklyanin, Smirnov, and Takhtajan, §7.1 by M. A. Semenov- Tian-Shansky, §§7.2–7.6 by Takhtajan and S. L. Shatashvili, §7.7 by A. Yu. Alekseev and Shatashvili, and §8 by I. Ya. Aref'eva.

We study instant conformal symmetry breaking as a holographic effect of ultrarelativistic particles moving in the AdS3 space–time. We give a qualitative picture of this effect based on calculating the two-point correlation functions and the entanglement entropy of the corresponding boundary theory. We show that in the geodesic approximation, because of gravitational lensing of the geodesics, the ultrarelativistic massless defect produces a zone structure for correlators with broken conformal invariance. At the same time, the holographic entanglement entropy also exhibits a transition to nonconformal behavior. Two colliding massless defects produce a more diverse zone structure for correlators and the entanglement entropy.

We study the large $N$ saddle points of two SYK chains coupled by an interaction that is nonlocal in Euclidean time. We start from analytic treatment of the free case with $q=2$ and perform the numerical study of the interacting case $q=4$. We show that in both cases there is a nontrivial phase structure with infinite number of phases. Every phase correspond to a saddle point in the non-interacting two-replica SYK. The nontrivial saddle points have non-zero value of the replica-nondiagonal correlator in the sense of quasi-averaging, when the coupling between replicas is turned off. Thus, the nonlocal interaction between replicas provides a protocol for turning the nonperturbatively subleading effects in SYK into non-equilibrium configurations which dominate at large $N$. For comparison we also study two SYK chains with local interaction for $q=2$ and $q=4$. We show that the $q=2$ model also has a similar phase structure, whereas in the $q=4$ model, dual to the traversable wormhole, the phase structure is different., Comment: 29 pages, 23 figures

The geodesics prescription in the holographic approach in the Lorentzian signature is applicable only for geodesics connecting spacelike-separated points at the boundary because there are no timelike geodesics that reach the boundary. Also, generally speaking, there is no direct analytic Euclidean continuation for a general background, such as a moving particle in the AdS space. We propose an improved geodesic image method for two-point Lorentzian correlators that is applicable for arbitrary time intervals when the space–time is deformed by point particles. We show that such a prescription agrees with the case where the analytic continuation exists and also with the previously used prescription for quasigeodesics. We also discuss some other applications of the improved image method: holographic entanglement entropy and multiple particles in the AdS3 space.

We study correlation functions of scalar operators on the boundary of the AdS3 space deformed by moving massive particles in the context of the AdS/CFT duality. To calculate two-point correlation functions, we use the geodesic approximation and the renormalized image method, obtained from the traditional image method with the renormalization taken into account. We compare results obtained using the renormalized image method with direct calculations using tracing of winding geodesics around the cone singularities. Examples demonstrate that the results coincide. We show that correlators in the geodesic approximation have a zone structure, which depends substantially on the particle mass and velocity.

Nonperturbative formulation of the Sachdev-Ye-Kitaev (SYK) model is discussed. The partition function of the model can be represented as a functional integral over the Grassmann variables in Euclidean time which is well defined but it diverges after the transformation to the fermion bilocal fields. We point out that the generating functional of the SYK model in real time is well defined even after the transformation to the bilocal fields and it can be used for nonperturbative investigations of its properties. The SYK model in zero dimensions is studied, its large N expansion is evaluated and phase transitions are investigated., LaTex, 18 pages, 4 figures

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., 39 pages, 12 figures; v3: typos corrected, to appear in Nucl. Phys. B

We consider the problem of excitation energy transfer in quantum many-particle systems with a dipole interaction. The considered exciton transfer mechanism is based on quantum interference. We show that by a special choice of interaction parameters, an enhancement of the exciton transfer to a sink and suppression of the transfer to alternative sinks can be achieved. The enhancement is proportional to the number of particles in the system. We use the quantum stochastic limit method to describe the dynamics. We indicate possible applications of the proposed mechanism to quantum processes in photosynthesis.

Covariant string field theory at finite temperature using quantum double (thermofield dynamics) formalism is considered. Thermal p-adic string theory amplitudes and a natural generalization of p-adic string effective action to the case on non-zero temperature are proposed.

We study holographic thermalization of a strongly coupled theory inspired by two colliding shock waves in a vacuum confining background. Holographic thermalization means a black hole formation, in fact a trapped surface formation. As a vacuum confining background we considered a well know bottom-up AdS/QCD model that provides the Cornell potential as well as reproduces QCD beta-function. We perturb vacuum background by colliding domain shock waves, that are assumed to be holographically dual to heavy ions collisions. Our main physical assumption is that we can make a restriction on the time of a trapped surface production that makes a natural limitation on the size of the domain where the trapped surface is produced. This limits the intermediate domain where the main part of the entropy is produced. In this domain one can use an intermediate vacuum background as an approximation to the full confining background. In this intermediate background a dependence of the produced entropy on colliding energy is very similar to the experimental dependence of particles multiplicities on colliding ions energy obtained from RHIC and LHC. This permits us to conclude that the entropy produced in collisions of domain shock waves during a short time models rather well the experimental data., Comment: 14 pages, 8 figures. v2: few remarks, one ref. and one figure added. v3: minor corrections and clarifications in sections 3 and 5

We consider a moving conical defect in the pure AdS3 space-time and calculate two-point correlation functions of a corresponding two-dimensional boundary quantum field theory in the geodesic approximation. We show that the presence of the defect leads to a gravitational lensing of geodesics, and this results in a finite number of similar terms in the Green’s function that correspond to winding geodesics in the bulk around the conical singularity. We show that for the quantized deficit angle γ = π/2n, the lensing produces domain wall excitations in the spectrum of the boundary theory.

We consider a holographic model of the heating up process. As a dual background we take a geometry describing thin shell accretion on a black brane. We find explicitly the time evolution of the mutual information during the non-equlibrium heating process from the initial temperature $T_i$ to the final temperature $T_f$ for the system of two intervals in the 1+1 dimensional case. We calculate widths and separation of twointervals for which the time dependence of the mutual information has the bell-like form, i.e. it starts from zero value at the wake up time, then reaches a maximal value and vanishes at the scrambling time. This form of the mutual information evolution was previously found in photosynthesis. The zone of the bell-like configurations exists for small distances $x>\log 2/2\pi T_i$, it exists only for large enough interval sizes and this zone becomes more narrow when $T_i$ increases and becomes larger with increasing of $T_f$., Comment: 17 pages, 9 figures. v2: typos corrected; references added

We study quark-antiquark potential using the AdS/CFT correspondence in the BTZ black hole with non-zero angular momentum. Using explicit form of string configurations relevant to a calculation of the potential we find that the potential exhibits different dependencies on angular momentum values in the Euclidean and the Lorentzian signatures of the BTZ., Comment: LaTex, 18 pages, 10 figures

A model of quantum field theory in an accelerated frame of reference is considered. It was suggested by Unruh that a uniformly accelerated detector in vacuum would perceive a noise with a thermal Gibbsian distribution. However, in justifying the assertion a singular transformation was implicitly performed, and doubts were expressed by some researches. We discuss a model of quantum field theory in an accelerated frame of reference in the two-dimensional spacetime for the wave equation. By using the Mellin transform, we obtain a representation of solutions of the wave equation. The representation includes a dependence on a parameter. The Unruh field corresponds to a singular limit of the representation.

We consider two holographically related theories. As the first (d + 1)-dimensional theory, we consider a model in which the (d + 1)-dimensional space is the direct product of ℝd and the half-axis ℝ+ and in which the kinetic operator has a nonlocal term induced by the nonlocal kinetic operator of the p-adic effective action. It turns out that the kinetic operator in the second, holographically related, d-dimensional theory is the kinetic operator of the string field theory effective action.

We investigate the relation between dilaton potentials and the b-factors of modified anti-de Sitter spaces and obtain the explicit form of dilaton potentials corresponding to b-factors that lead to a satisfactory description of the particle creation multiplicity in the framework of the holographic description.

We review recent applications of the dual holographic approach to describing the quark–gluon plasma observed in high-energy collisions of relativistic heavy nuclei. Holography and AdS/CFT duality provide a means to study the properties of strong-coupling quantum field theories using higher-dimensional gravity theories. The appearance of quark–gluon plasma in heavy ion collisions can be described in dual terms as the formation of a black hole. To illustrate the major achievements of holographic theory, we discuss the calculation of the following quantities: the shear viscosity and other transport coefficients (all calculated by second order hydrodynamic models), the energy dependence of multiplicities, and the anisotropic thermalization and isotropization times. We also compare theoretical predictions with available experimental data, including the recent LHC results.

The quark-gluon plasma formed as a result of heavy-ion collisions is currently investigated actively both theoretically and experimentally. According to the holographic approach, forming a quark-gluon plasma in the four-dimensional world is associated with creating black holes in a five-dimensional anti-de Sitter space. The multiplicity of particles produced in heavy-ion collisions is then determined by the entropy of the five-dimensional black hole, which is estimated by the area of the trapped surface. To fit the experimental data for multiplicity Kiritsis and Taliotis have proposed to consider black holes formation in modified ${AdS}_5$ spaces with different $b$-factors. In this paper we consider the formation of black holes under collision of membranes in modified ${AdS}_5$ spaces with $b$-factors. Following the previous proposals we consider the power-law and exponential $b$-factors, as well as mixed types of $b$-factors. We study dynamics of the change of the trapped surface area depending on the energy for each investigated space. We find that the power-law and mixed factors fit better to the experimental date.

We consider the transition of a quantum field system toward the state of thermal equilibrium based on the holographic description using the duality between the quantum field system in the d-dimensional Minkowski space and the gravity theory in the (d+1)-dimensional anti-de Sitter space. In this construction, the thermalization in the d-dimensional space is described in the holographic language as the formation of a black hole in the (d+1)-dimensional space. We use a holographic model of thermalization of the quark-gluon plasma describing the black hole formation by the Vaidya metric. We show that evaporation of the black hole, also modeled by the Vaidya metric, leads to an interesting effect in the d-dimensional space: thermalization occurs only at small distances and is impossible in the infrared region. In the considered model, the thermal behavior at small distances is possible only during a certain time, after which the dethermalization process begins.

We discuss the classical aspects of dynamics of scalar models with non-positive Higgs potentials in the FRW cosmology. These models appear as effective local models in non-local models related with string field theories. After a suitable field redefinition these models have the form of local Higgs models with a negative extra cosmological term and the total Higgs potential is non-positively defined and has rather small coupling constant. The non-positivity of the potential leads to the fact that on some stage of evolution the expansion mode gives place to the mode of contraction, due to that the stage of reheating is absent. In these models the hard regime of inflation gives place to inflation near the hill top and the area of the slow roll inflation is very small. Meanwhile one can obtain enough e-foldings before the contraction to make the model under consideration admissible to describe inflation.

Asymptotic methods in the theory of differential equations and in nonlinear mechanics are commonly used to improve perturbation theory in the small oscillation regime. However, in some problems of nonlinear dynamics, in particular for the Higgs equation in field theory, it is important to consider not only small oscillations but also the rolling regime. In this article we consider the Higgs equation and develop a hyperbolic analogue of the averaging method. We represent the solution in terms of elliptic functions and, using an expansion in hyperbolic functions, construct an approximate solution in the rolling regime. An estimate of accuracy of the asymptotic expansion in an arbitrary order is presented.

Asymptotic methods in nonlinear dynamics are used to improve perturbation theory results in the oscillations regime. However, for some problems of nonlinear dynamics, particularly in the case of Higgs (Duffing) equation and the Friedmann cosmological equations, not only small oscillations regime is of interest but also the regime of rolling (climbing), more precisely the rolling from a top (climbing to a top). In the Friedman cosmology, where the slow rolling regime is often used, the rolling from a top (not necessary slow) is of interest too. In the present work a method for approximate solution to the Higgs equation in the rolling regime is presented. It is shown that in order to improve perturbation theory in the rolling regime turns out to be effective not to use an expansion in trigonometric functions as it is done in case of small oscillations but use expansions in hyperbolic functions instead. This regime is investigated using the representation of the solution in terms of elliptic functions. An accuracy of the corresponding approximation is estimated., Latex, 36 Pages, 8 figures, typos corrected

The paper presents recent achievements and open questions in string field theory that are related to the cohomology of BRST operators. We sketch the construction of a nonpolynomial action based on cubic theory that uses the triviality of the BRST operator in the so-called large algebra. We also construct special solutions of equations of motion in superstring field theory and study the cohomology of a modified BRST operator near these solutions.

We regard an ultrarelativistic hadron moving on a brane embedded in a higher-dimensional space-time as a membrane propagating on a three-brane. For hadron sizes exceeding the compactification radius and characteristic scales of five-dimensional gravitational interaction, this membrane can be regarded as a cosmic membrane in the sense that it extends to the infinities. In the five-dimensional case, a cosmic membrane produces a topological defect similar to the defect produced by a cosmic string in the four-dimensional space-time. This representation allows calculating the effects of the influence of the hadron mass on the gravitational interaction of partons belonging to the colliding hadrons.

We discuss various mechanisms of catalysis of black holes/wormholes (BH/WH) formation in particles collisions. The current paradigm suggests that BH/WH formation in particles collisions will happen when center of mass energies of colliding particles is sufficiently above the Planck scale (the transplanckian region). To estimate the BH/WH production we use the classical geometrical cross section. We confirm the classical geometrical cross section of the BH production reconsidering the process of two transplanckian particles collision in the rest frame of one of incident particles. This consideration permits to use the standard Thorne's hoop conjecture for a matter compressed into a region to prove a variant of the conjecture dealing with a total amount of compressed energy in the case of colliding particles. We calculate geometrical cross sections for different processes and for different background, in particular, for (A)dS. We show that results are in agreement with closed trapped surface (CTS) estimations though there are no general theorems providing that the BH formation follows from CTS's formation. We show that the process of BH formation is catalyzed by the negative cosmological constant and by a particular scalar matter, namely dilaton, while it is relaxed by the positive cosmological constant and at a critical value just turns off. Also we note that the cross section is sensible to the compactification of extra dimensions and to the particular brane model., Comment: LaTex, 43 pages, 12 figures, Extended version of the talk at the International Bogoliubov Conference "Problems of Theoretical and Mathematical Physics", Moscow-Dubna, August 21-27, 2009

We review recent achievements and open questions in string field theory. We comment on the history of the construction of the covariant gauge-invariant string field formulation and briefly consider possible applications of string field theory in D-brane physics and cosmology.

We discuss various mechanisms of catalysis of black holes/wormholes (BH/WH) formation in particles collisions. The current paradigm suggests that BH/WH formation in particles collisions will happen when center of mass energies of colliding particles is sufficiently above the Planck scale (the transplanckian region). To estimate the BH/WH production we use the classical geometrical cross section. We confirm the classical geometrical cross section of the BH production reconsidering the process of two transplanckian particles collision in the rest frame of one of incident particles. This consideration permits to use the standard Thorne's hoop conjecture for a matter compressed into a region to prove a variant of the conjecture dealing with a total amount of compressed energy in the case of colliding particles. We calculate geometrical cross sections for different processes and for different background, in particular, for (A)dS. We show that results are in agreement with closed trapped surface (CTS) estimations though there are no general theorems providing that the BH formation follows from CTS's formation. We show that the process of BH formation is catalyzed by the negative cosmological constant and by a particular scalar matter, namely dilaton, while it is relaxed by the positive cosmological constant and at a critical value just turns off. Also we note that the cross section is sensible to the compactification of extra dimensions and to the particular brane model.

Special perturbative pure gauge solutions parameterized by a pair of wedge states are parts of the nontrivial (not purely gauge) tachyon solutions of the cubic fermionic string field theory describing the non-BPS brane true vacuum. We demonstrate explicitly that for the large parameter of the perturbation expansion, these pure gauge configurations are no longer solutions of the equations of motion. We show that this problem is solved by adding an extra term that is just the term needed for the first Sen conjecture to hold.

We clarify the relationship between Schnabl’s solution and pure gauge configurations. Both Schnabl’s and pure gauge solutions are obtained by means of an iterative procedure. We show that the pure gauge string field configuration that is used in the construction of a perturbation series for Schnabl’s solution diverges on a large subspace of string configurations, but it can be rendered convergent by adding a compensating term. The additional term ensures the fulfillment of the equations of motion in a weak sense. This compensating term coincides with the term necessary for obtaining an action consistent with Sen’s first conjecture.

We demonstrate that vacuum solutions in the Neveu-Schwarz field theory of a fermionic string incorporating the GSO(−) sector are naturally related to the zero-curvature representation in a graded space of special form. We use the same representation to describe the equivalence of the cubic and nonpolynomial theories with the GSO(−) sector also taken into account.

Recently, black hole and brane production at CERN's Large Hadron Collider (LHC) has been widely discussed. We suggest that there is a possibility to test causality at the LHC. We argue that if the scale of quantum gravity is of the order of few TeVs, proton-proton collisions at the LHC could lead to the formation of time machines (spacetime regions with closed timelike curves) which violate causality. One model for the time machine is a traversable wormhole. We argue that the traversable wormhole production cross section at the LHC is of the same order as the cross section for the black hole production. Traversable wormholes assume violation of the null energy condition (NEC) and an exotic matter similar to the dark energy is required. Decay of the wormholes/time machines and signatures of time machine events at the LHC are discussed., 12 pages, LATEX, comments and references added

Field theories which violate the null energy condition (NEC) are of interest for the solution of the cosmological singularity problem and for models of cosmological dark energy with the equation of state parameter $w, Comment: 13 pages, Latex, 1 figure

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and the Langlands program is indicated. The Beilinson conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed., 14 pages, corrected typos, references and comments added

We reexamine the oscillator level truncation method in the bosonic String Field Theory (SFT) by calculation the descent relation =Z_3, Comment: 21 pages, 10 figures, Latex

We introduce the quadratic Fermi algebra, which is a Lie algebra, and calculate the vacuum distributions of the associated Hamiltonians. In order to emphasize the difference with the Bose case, we apply a modification of the method used in the above calculation to obtain a simple and straightforward classification of the 1-dimensional Meixner laws in terms of homogeneous quadratic expressions in the Bose creation and annihilation operators. There is a huge literature of the Meixner laws but this, purely quantum probabilistic, derivation seems to be new. Finally we briefly discuss the possible multidimensional extensions of the above results.