Generalized Fubini instantons

We show that $(1+2)$ nonlinear Klein-Gordon equation with negative coupling admits an exact solution which appears to be the linear superposition of the plane wave and the nonsingular rational soliton. We show that the same approach allows to construct the solution of similar properties for the Euclidean $\phi^4$ model with broken symmetry. Interestingly, this regular solution will be of instanton type only in the $D\le 5$ Euclidean space.Comment: 10 page

Cosmic Strings on the Lattice

We develop a formalism for the quantization of topologically stable excitations in the 4-dimensional abelian lattice gauge theory. The excitations are global and local (Abrikosov-Nielsen-Olesen) strings and monopoles. The operators of creation and annihilation of string states are constructed; the string Green functions are represented as a path integral over random surfaces. Topological excitations play an important role in the early universe. In the broken symmetry phase of the $U(1)$ spin model, closed global cosmic strings arise, while in the Higgs phase of the noncompact gauge-Higgs model, local cosmic strings are present. The compact gauge-Higgs model also involves monopoles. Then the strings can break if their ends are capped by monopoles. The topology of the Euclidean string world sheets are studied by numerical simulations.Comment: 4 pages LaTex (espcrc2.sty), LATTICE'92 contribution, ITEP(1992

Chiral Vortical Effect in Fermi Liquid

In this note we consider non-relativistic rotating fermi liquid in the presence of Berry curvature. The behavior of the system is then almost the same as in external magnetic field. We argue that there appears an analogue of chiral vortical effect in the liquid if Berry curvature has a non-vanishing flux through sheets of Fermi surfaces and chemical potentials are different. We also claim that quantum anomalies in condensed matter context provide a theoretical and experimental testing ground for the origin of chiral effects, their carriers etc.Comment: minor corrections, additional citation

Ultimate gravitational mass defect

We present a new type of gravitational mass defect in which an infinite amount of matter may be bounded in a zero ADM mass. This interpolates between effects typical of closed worlds and T-spheres. We consider the Tolman model of dust distribution and show that this phenomenon reveals itself for a solution that has no origin on one side but is closed on the other side. The second class of examples corresponds to smooth gluing T-spheres to the portion of the Friedmann-Robertson-Walker solution. The procedure is generalized to combinations of smoothly connected T-spheres, FRW and Schwarzschild metrics. In particular, in this approach a finite T-sphere is obtained that looks for observers in two R-regions as the Schwarzschild metric with two different masses one of which may vanish.Comment: 9 pages. 1 reference added. To appear in Gen. Rel. Gra

Energy flux through the horizon in the black hole-domain wall systems

We study various configurations in which a domain wall (or cosmic string), described by the Nambu-Goto action, is embedded in a background space-time of a black hole in $(3+1)$ and higher dimensional models. We calculate energy fluxes through the black hole horizon. In the simplest case, when a static domain wall enters the horizon of a static black hole perperdicularly, the energy flux is zero. In more complicated situations, where parameters which describe the domain wall surface are time and position dependent, the flux is non-vanishing is principle. These results are of importance in various conventional cosmological models which accommodate the existence of domain walls and strings and also in brane world scenarios.Comment: references added, accepted for publication in JHE

Resonant structure of space-time of early universe

A new fully quantum method describing penetration of packet from internal well outside with its tunneling through the barrier of arbitrary shape used in problems of quantum cosmology, is presented. The method allows to determine amplitudes of wave function, penetrability $T_{\rm bar}$ and reflection $R_{\rm bar}$ relatively the barrier (accuracy of the method: $|T_{\rm bar}+R_{\rm bar}-1| < 1 \cdot 10^{-15}$), coefficient of penetration (i.e. probability of the packet to penetrate from the internal well outside with its tunneling), coefficient of oscillations (describing oscillating behavior of the packet inside the internal well). Using the method, evolution of universe in the closed Friedmann--Robertson--Walker model with quantization in presence of positive cosmological constant, radiation and component of generalize Chaplygin gas is studied. It is established (for the first time): (1) oscillating dependence of the penetrability on localization of start of the packet; (2) presence of resonant values of energy of radiation $E_{\rm rad}$, at which the coefficient of penetration increases strongly. From analysis of these results it follows: (1) necessity to introduce initial condition into both non-stationary, and stationary quantum models; (2) presence of some definite values for the scale factor $a$, where start of expansion of universe is the most probable; (3) during expansion of universe in the initial stage its radius is changed not continuously, but passes consequently through definite discrete values and tends to continuous spectrum in latter time.Comment: 18 pages, 14 figures, 4 table

Quantum Group and Magnetic Translations. Bethe-Ansatz Solution for Azbel-Hofstadter Problem

We present a new approach to the problem of Bloch electrons in magnetic ( sometimes called Azbel-Hofstadter problem) field, by making explicit a natural relation between the group of magnetic translations and the quantum group $U_{q}(sl_2)$. The approach allows us to express the "mid" band spectrum of the model and the Bloch wave function as solutions of the Bethe-Ansatz equations typical for completely integrable quantum systems. The zero mode wave functions are found explicitly in terms of $q$-deformed classical orthogonal polynomials.In this paper we present solution for the isotropic problem. We also present a class of solvable quasiperiodic equations related to $U_{q}(sl_2)$.Comment: 19 pages, Revte

Comparative study of loop contributions in AdS and dS

The generic feature of non-conformal fields in Poincare patch of de Sitter space is the presence of large IR loop corrections even for massive fields. Moreover, in global de Sitter there are loop IR divergences for the massive fields. Naive analytic continuation from de Sitter to Anti-de-Sitter might lead one to conclude that something similar should happen in the latter space as well. However, we show that there are no large IR effects in the one-loop two-point functions in the Poincare patch of Anti-de-Sitter space even for the zero mass minimally coupled scalar fields. As well there are neither large IR effects nor IR divergences in global Anti-de-Sitter space even for the zero mass.Comment: 12 pages. Minor changes, misprints are correcte

An Infrared Divergence Problem in the cosmological measure theory and the anthropic reasoning

An anthropic principle has made it possible to answer the difficult question of why the observable value of cosmological constant ($\Lambda\sim 10^{-47}$ GeV${}^4$) is so disconcertingly tiny compared to predicted value of vacuum energy density $\rho_{SUSY}\sim 10^{12}$ GeV${}^4$. Unfortunately, there is a darker side to this argument, as it consequently leads to another absurd prediction: that the probability to observe the value $\Lambda=0$ for randomly selected observer exactly equals to 1. We'll call this controversy an infrared divergence problem. It is shown that the IRD prediction can be avoided with the help of a Linde-Vanchurin {\em singular runaway measure} coupled with the calculation of relative Bayesian probabilities by the means of the {\em doomsday argument}. Moreover, it is shown that while the IRD problem occurs for the {\em prediction stage} of value of $\Lambda$, it disappears at the {\em explanatory stage} when $\Lambda$ has already been measured by the observer.Comment: 9 pages, RevTe

Chiral Magnetic Effect in Hydrodynamic Approximation

We review derivations of the chiral magnetic effect (ChME) in hydrodynamic approximation. The reader is assumed to be familiar with the basics of the effect. The main challenge now is to account for the strong interactions between the constituents of the fluid. The main result is that the ChME is not renormalized: in the hydrodynamic approximation it remains the same as for non-interacting chiral fermions moving in an external magnetic field. The key ingredients in the proof are general laws of thermodynamics and the Adler-Bardeen theorem for the chiral anomaly in external electromagnetic fields. The chiral magnetic effect in hydrodynamics represents a macroscopic manifestation of a quantum phenomenon (chiral anomaly). Moreover, one can argue that the current induced by the magnetic field is dissipation free and talk about a kind of "chiral superconductivity". More precise description is a ballistic transport along magnetic field taking place in equilibrium and in absence of a driving force. The basic limitation is exact chiral limit while the temperature--excitingly enough- does not seemingly matter. What is still lacking, is a detailed quantum microscopic picture for the ChME in hydrodynamics. Probably, the chiral currents propagate through lower-dimensional defects, like vortices in superfluid. In case of superfluid, the prediction for the chiral magnetic effect remains unmodified although the emerging dynamical picture differs from the standard one.Comment: 35 pages, prepared for a volume of the Springer Lecture Notes in Physics "Strongly interacting matter in magnetic fields" edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye