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Mikhail S. Volkov

Publications and source records attributed to Mikhail S. Volkov.

At least 55 records · Page 3Linked to original sources
arXiv2009

Spinning Electroweak Sphalerons

We present numerical evidence for the existence of stationary spinning generalizations for the static sphaleron in the Weinberg-Salam theory. Our results suggest that, for any value of the mixing angle $\thetw$ and for any Higgs mass, the spinning sphalerons comprise a family labeled by their angular momentum $J$. For $\thetw\neq 0$ they possess an electric charge $Q=eJ$ where $e$ is the electron charge. Inside they contain a monopole-antimonopole pair and a spinning loop of electric current, and for large $J$ they show a Regge-type behavior. It is likely that these sphalerons mediate the topological transitions in sectors with $J\neq 0$, thus enlarging the number of transition channels. Their action {\it decreases} with $J$, which may considerably affect the total transition rate.

hep-th↗
arXiv2009

Superconducting non-Abelian vortices in Weinberg-Salam theory -- electroweak thunderbolts

We present a detailed analysis of classical solutions in the bosonic sector of the electroweak theory which describe vortices carrying a constant electric current ${\cal I}$. These vortices exist for any value of the Higgs boson mass and for any weak mixing angle, and in the zero current limit they reduce to Z strings. Their current is produced by the condensate of vector W bosons and typically it can attain billions of Amperes. For large ${\cal I}$ the vortices show a compact condensate core of size $\sim 1/{\cal I}$, embedded into a region of size $\sim{\cal I}$ where the electroweak gauge symmetry is completely restored, followed by a transition zone where the Higgs field interpolates between the symmetric and broken phases. Outside this zone the fields are the same as for the ordinary electric wire. An asymptotic approximation of the large ${\cal I}$ solutions suggests that the current can be {arbitrarily} large, due to the scale invariance of the vector boson condensate. Finite vortex segments whose length grows with ${\cal I}$ seem to be perturbatively stable. This suggests that they can transfer electric charge between different regions of space, similarly to thunderbolts. It is also possible that they can form loops stabilized by the centrifugal force -- electroweak vortons.

hep-th↗
arXiv2008

Stationary ring solitons in field theory - knots and vortons

We review the current status of the problem of constructing classical field theory solutions describing stationary vortex rings in Minkowski space in 3+1 dimensions. We describe the known up to date solutions of this type, such as the static knot solitons stabilized by the topological Hopf charge, the attempts to gauge them, the anomalous solitons stabilized by the Chern-Simons number, as well as the non-Abelian monopole and sphaleron rings. Passing to the rotating solutions, we first discuss the conditions insuring that they do not radiate, and then describe the spinning $Q$-balls, their twisted and gauged generalizations reported here for the first time, spinning skyrmions, and rotating monopole-antimonopole pairs. We then present the first explicit construction of global vortons as solutions of the elliptic boundary value problem, which demonstrates their non-radiating character. Finally, we describe the analogs of vortons in the Bose-Einstein condensates, analogs of spinning $Q$-balls in the non-linear optics, and also moving vortex rings in superfluid helium and in ferromagnetics.

hep-th↗
arXiv2008

Stability Analysis of The Twisted Superconducting Semilocal Strings

We study the stability properties of the twisted vortex solutions in the semilocal Abelian Higgs model with a global $\mathbf{SU}(2)$ invariance. This model can be viewed as the Weinberg-Salam theory in the limit where the non-Abelian gauge field decouples, or as a two component Ginzburg-Landau theory. The twisted vortices are characterized by a constant global current ${\cal I}$, and for ${\cal I}\to 0$ they reduce to the semilocal strings, that is to the Abrikosov-Nielsen-Olesen vortices embedded into the semilocal model. Solutions with ${\cal I}\neq 0$ are more complex and, in particular, they are {\it less energetic} than the semilocal strings, which makes one hope that they could have better stability properties. We consider the generic field fluctuations around the twisted vortex within the linear perturbation theory and apply the Jacobi criterion to test the existence of the negative modes in the spectrum of the fluctuation operator. We find that twisted vortices do not have the homogeneous instability known for the semilocal strings, neither do they have inhomogeneous instabilities whose wavelength is less than a certain critical value. This implies that short enough vortex pieces are perturbatively stable and suggests that small vortex loops could perhaps be stable as well. For longer wavelength perturbations there is exactly one negative mode in the spectrum whose growth entails a segmentation of the uniform vortex into a non-uniform, `sausage like' structure. This instability is qualitatively similar to the hydrodynamical Plateau-Rayleigh instability of a water jet or to the Gregory-Laflamme instability of black strings in the theory of gravity in higher dimensions.

hep-th↗
arXiv2007

Superconducting Electroweak Strings

Classical solutions describing strings endowed with an electric charge and carrying a constant electromagnetic current are constructed within the bosonic sector of the Electroweak Theory. For any given ratio of the Higgs boson mass to W boson mass and for any Weinberg's angle, these strings comprise a family that can be parameterized by values of the current through their cross section, $I_3$, by their electric charge per unit string length, $I_0$, and by two integers. These parameters determine the electromagnetic and Z fluxes, as well as the angular momentum and momentum densities of the string. For $I_0\to 0$ and $I_3\to 0$ the solutions reduce to Z strings, or, for solutions with $I_0=\pm I_3$, to the W-dressed Z strings whose existence was discussed some time ago.

hep-th↗
arXiv2006

Gravitating non-Abelian solitons and hairy black holes in higher dimensions

This is a short review of classical solutions with gravitating Yang-Mills fields in $D>4$ spacetime dimensions. The simplest SO(4) symmetric particlelike and SO(3) symmetric vortex type solutions in the Einstein-Yang-Mills theory in D=5 are considered, and their various generalizations with or without an event horizon, for other symmetries, in more general theories, and also in $D>5$ are described. In addition, supersymmetric solutions with gravitating Yang-Mills fields in string theory are discussed.

hep-th↗
arXiv2006

Einstein--Yang--Mills strings

We present globally regular vortex-type solutions for a pure SU(2) Yang-Mills field coupled to gravity in 3+1 dimensions. These gravitating vortices are static, cylindrically symmetric and purely magnetic, and they support a non-zero chromo-magnetic flux through their cross section. In addition, they carry a constant non-Abelian current, and so in some sense they are analogs of the superconducting cosmic strings. They have a compact central core dominated by a longitudinal magnetic field and endowed with an approximately Melvin geometry. This magnetic field component gets color screened in the exterior part of the core, outside of which the fields approach exponentially fast those of the electrovacuum Bonnor solutions with a circular magnetic field. In the far field zone the solutions are not asymptotically flat but tend to vacuum Kasner metrics.

hep-th↗
arXiv2006

Twisted Superconducting Semilocal Strings

A new class of twisted, current carrying, stationary, straight string solutions having finite energy per unit length is constructed numerically in an extended Abelian Higgs model with global SU(2) symmetry. The new solutions correspond to deformations of the embedded Abrikosov-Nielsen-Olesen (ANO) vortices by a twist -- a relative coordinate dependent phase between the two Higgs fields. The twist induces a global current flowing through the string, and the deformed solutions bifurcate with the ANO vortices in the limit of vanishing current. For each value of the winding number $n=1,2...$ (determining the magnetic flux through the plane orthogonal to the string) there are $n$ distinct, two-parametric families of solutions. One of the continuously varying parameters is the twist, or the corresponding current, the other one can be chosen to be the momentum of the string. For fixed values of the momentum and twist, the $n$ distinct solutions have different energies and can be viewed as a lowest energy ``fundamental'' string and its $n-1$ ``excitations'' characterized by different values of their ``polarization''. The latter is defined as the ratio of the angular momentum of the vortex and its momentum. In their rest frame the twisted vortices have lower energy than the embedded ANO vortices and could be of considerable importance in various physical systems (from condensed matter to cosmic strings).

hep-th↗
arXiv2004

Regular non-Abelian vacua in ${\cal N}=4$, SO(4) gauged supergravity

We present a family of globally regular ${\cal N}=1$ vacua in the D=4, ${\cal N}=4$ gauged supergravity of Gates and Zwiebach. These solutions are labeled by the ratio $ξ$ of the two gauge couplings, and for $ξ=0$ they reduce to the supergravity monopole previously used for constructing the gravity dual of ${\cal N}=1$ super Yang-Mills theory. For $ξ>0$ the solutions are asymptotically anti de Sitter, but with an excess of the solid angle, and they reduce exactly to anti de Sitter for $ξ=1$. Solutions with $ξ<0$ are topologically $R^1\times S^3$, and for $ξ=-2$ they become $R^1\times S^3$ geometrically. All solutions with $ξ\neq 0$ can be promoted to D=11 to become vacua of M-theory.

hep-th↗
arXiv2003

Resonant excitations of the 't Hooft-Polyakov monopole

The spherically symmetric magnetic monopole in an SU(2) gauge theory coupled to a massless Higgs field is shown to possess an infinite number of resonances or quasinormal modes. These modes are eigenfunctions of the isospin 1 perturbation equations with complex eigenvalues, $E_n=ω_n-iγ_n$, satisfying the outgoing radiation condition. For $n\to\infty$, their frequencies $ω_n$ approach the mass of the vector boson, $M_W$, while their lifetimes $1/γ_n$ tend to infinity. The response of the monopole to an arbitrary initial perturbation is largely determined by these resonant modes, whose collective effect leads to the formation of a long living breather-like excitation characterized by pulsations with a frequency approaching $M_W$ and with an amplitude decaying at late times as $t^{-5/6}$.

hep-th↗
arXiv2003

Existence of spinning solitons in gauge field theory

We study the existence of classical soliton solutions with intrinsic angular momentum in Yang-Mills-Higgs theory with a compact gauge group $\mathcal{G}$ in (3+1)-dimensional Minkowski space. We show that for \textit{symmetric} gauge fields the Noether charges corresponding to \textit{rigid} spatial symmetries, as the angular momentum, can be expressed in terms of \textit{surface} integrals. Using this result, we demonstrate in the case of $\mathcal{G}=SU(2)$ the nonexistence of stationary and axially symmetric spinning excitations for all known topological solitons in the one-soliton sector, that is, for 't Hooft--Polyakov monopoles, Julia-Zee dyons, sphalerons, and also vortices.

hep-th↗
arXiv2002

Spinning Q-Balls

We present numerical evidence for the existence of spinning generalizations for non-topological Q-ball solitons in the theory of a complex scalar field with a non-renormalizable self-interaction. To the best of our knowledge, this provides the first explicit example of spinning solitons in 3+1 dimensional Minkowski space. In addition, we find an infinite discrete family of radial excitations of non-rotating Q-balls, and construct also spinning Q-balls in 2+1 dimensions.

hep-th↗
arXiv2002

The Semiclassical Instability of de Sitter Space

The effect of the spontaneous nucleation of black holes in de Sitter space is reviewed, and the main steps of the calculation in Nucl.Phys. B 582, 313, 2000 of the one-loop amplitude of this process are summarized. The existence of such an effect suggests that de Sitter space is not a ground state of quantum gravity with a positive cosmological constant.

hep-th↗
arXiv2001

Gravitating Yang-Mills vortices in 4+1 spacetime dimensions

The coupling to gravity in D=5 spacetime dimensions is considered for the particle-like and vortex-type solutions obtained by uplifting the D=4 Yang-Mills instantons and D=3 Yang-Mills-Higgs monopoles. It turns out that the particles become completely destroyed by gravity, while the vortices admit a rich spectrum of gravitating generalizations. Such vortex defects may be interesting in view of the AdS/CFT correspondence or in the context of the brane world scenario.

hep-th↗
arXiv2001

Non-abelian 4-d black holes, wrapped 5-branes, and their dual descriptions

We study extremal and non-extremal generalizations of the regular non-abelian monopole solution of hep-th/9707176, interpreted in hep-th/0007018 as 5-branes wrapped on a shrinking S^2. Naively, the low energy dynamics is pure N=1 supersymmetric Yang-Mills. However, our results suggest that the scale of confinement and chiral symmetry breaking in the Yang-Mills theory actually coincides with the Hagedorn temperature of the little string theory. We find solutions with regular horizons and arbitrarily high Hawking temperature. Chiral symmetry is restored at high energy density, corresponding to large black holes. But the entropy of the black hole solutions decreases as one proceeds to higher temperatures, indicating that there is a thermodynamic instability and that the canonical ensemble is ill-defined. For certain limits of the black hole solutions, we exhibit explicit non-linear sigma models involving a linear dilaton. In other limits we find extremal non-BPS solutions which may have some relevance to string cosmology.

hep-th↗
arXiv2001

Non-Abelian vacua in D=5, N=4 gauged supergravity

We study essentially non-Abelian backgrounds in the five dimensional N=4 gauged SU(2)$\times$U(1) supergravity. Static configurations that are invariant under either the SO(4) spatial rotations or with respect to the SO(3) rotations and translations along the fourth spatial coordinate are considered. By analyzing consistency conditions for the equations for supersymmetric Killing spinors we derive the Bogomol'nyi equations and obtain their globally regular solutions. The SO(4) symmetric configurations contain the purely magnetic non-Abelian fields together with the purely electric Abelian field and possess two unbroken supersymmetries. The SO(3) configurations have only the non-Abelian fields and preserve four supersymmetries.

hep-th↗
arXiv2000

Black hole pair creation in de Sitter space: a complete one-loop analysis

We present an exact one-loop calculation of the tunneling process in Euclidean quantum gravity describing creation of black hole pairs in a de Sitter universe. Such processes are mediated by $S^2\times S^2$ gravitational instantons giving an imaginary contribution to the partition function. The required energy is provided by the expansion of the universe. We utilize the thermal properties of de Sitter space to describe the process as the decay of a metastable thermal state. Within the Euclidean path integral approach to gravity, we explicitly determine the spectra of the fluctuation operators, exactly calculate the one-loop fluctuation determinants in the $ζ$-function regularization scheme, and check the agreement with the expected scaling behaviour. Our results show a constant volume density of created black holes at late times, and a very strong suppression of the nucleation rate for small values of $Λ$.

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