arXiv subjects

Mikhail S. Volkov

Publications and source records attributed to Mikhail S. Volkov.

68 records · Page 4Linked to original sources

arXiv2000

The tale of gravitational sphaleron

Type I string theory can be dimensionally reduced on group manifolds. The compactification on $S^3\times S^3$ leads to the N=4 gauged SU(2)$\times$SU(2) supergravity in four dimensions, which admits the BPS monopole type non-Abelian vacuum. The reduction on $S^3\times AdS_3$ gives the Euclidean N=4 gauged SU(2)$\times$SU(1,1) supergravity admitting a globally regular supersymmetric non-Abelian background. The latter can be analytically continued to the Lorentzian sector, which gives the regular, unstable particle-like configuration known as gravitational sphaleron. When lifted to D=10, the Euclidean vacuum describes a deformation of the D1--D5 brane system.

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arXiv1999

Gravitating Non-Abelian Solitons and Black Holes with Yang-Mills Fields

We present a review of gravitating particle-like and black hole solutions with non-Abelian gauge fields. The emphasis is given to the description of the structure of the solutions and to the connection with the results of flat space soliton physics. We describe the Bartnik-McKinnon solitons and the non-Abelian black holes arising in the Einstein-Yang-Mills theory, and their various generalizations. These include axially symmetric and slowly rotating configurations, solutions with higher gauge groups, $Λ$-term, dilaton, and higher curvature corrections. The stability issue is discussed as well. We also describe the gravitating generalizations for flat space monopoles, sphalerons, and Skyrmions.

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arXiv1999

Euclidean Freedman-Schwarz model

The N=4 gauged SU(2)$\times$SU(1,1) supergravity in four-dimensional Euclidean space is obtained via a consistent dimensional reduction of the N=1, D=10 supergravity on $S^3\times AdS_3$. The dilaton potential in the theory is proportional to the difference of the two gauge coupling constants, which is due to the opposite signs of the curvatures of $S^3$ and $AdS_3$. As a result, the potential can be positive, negative, or zero-depending on the values of the constants. A consistent reduction of the fermion supersymmetry transformations is performed at the linearized level, and special attention is paid to the Euclidean Majorana condition. A further reduction of the D=4 theory is considered to the static, purely magnetic sector, where the vacuum solutions are studied. The Bogomol'nyi equations are derived and their essentially non-Abelian monopole-type and sphaleron-type solutions are presented. Any solution in the theory can be uplifted to become a vacuum of string or M-theory.

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arXiv1999

Bogomol'nyi Equations for Einstein-Yang-Mills-Dilaton theory

A static, spherically symmetric and purely magnetic solution of the Einstein-Yang-Mills-Dilaton theory, found previously by numerical integration is shown to obey a system of first order Bogomol'nyi equations. As common for such equations, there is a tight relation to supersymmetry, in the present case to the N=4 gauged SU(2)$\times$SU(2) supergravity of Freedman and Schwarz. Specifically, the dilaton potential of the latter can be avoided by choosing one of the two gauge coupling constants to be imaginary. It is argued that this corresponds to a hitherto unknown N=4 gauged SU(2)$\times$SU(1,1) supergravity in four Euclidean dimensions leading to Bogomol'nyi equations with asymptotically flat solutions.

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arXiv1997

Non-Abelian Solitons in N=4 Gauged Supergravity and Leading Order String Theory

We study static, spherically symmetric, and purely magnetic solutions of the N=4 gauged supergravity in four dimensions. A systematic analysis of the supersymmetry conditions reveals solutions which preserve 1/4 of the supersymmetries and are characterized by a BPS-monopole-type gauge field and a globally hyperbolic, everywhere regular geometry. We show that the theory in which these solutions arise can be obtained via compactification of ten-dimensional supergravity on the group manifold. This result is then used to lift the solutions to ten dimensions.

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arXiv1997

Non-Abelian BPS Monopoles in N=4 Gauged Supergravity

We study static, spherically symmetric, and purely magnetic solutions of SU(2) $\times$ SU(2) gauge supergravity in four dimensions. A systematic analysis of the supersymmetry conditions reveals solutions which preserve 1/8 of the supersymmetries and are characterized by a BPS-monopole-type gauge field and a globally hyperbolic, everywhere regular geometry. These present the first known example of non-Abelian backgrounds in gauge supergravity and in leading order effective string theory.

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arXiv1997

Slowly Rotating Non-Abelian Black Holes

It is shown that the well-known non-Abelian static SU(2) black hole solutions have rotating generalizations, provided that the hypothesis of linearization stability is accepted. Surprisingly, this rotating branch has an asymptotically Abelian gauge field with an electric charge that cannot vanish, although the non-rotating limit is uncharged. We argue that this may be related to our second finding, namely that there are no globally regular slowly rotating excitations of the particle-like Bartnik-McKinnon solutions.

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arXiv1996

Sphaleron on $S^{3}$

An exactly solvable sphaleron model in $3+1$ spacetime dimensions is described

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arXiv1996

Negative modes around Einstein-Yang-Mills sphalerons and black holes

The dynamics of small perturbations around sphaleron and black hole solutions in the Einstein-Yang-Mills theory for the gauge group $SU(2)$ is investigated. The perturbations can be split into the two independent sectors in accordance with their parity; each sector contains negative modes. The even-parity negative modes are shown to correspond to the negative second variations of the height of the potential energy barrier near the sphaleron. For the odd-parity sector, the existence of precisely $n$ (the number of nodes of the sphaleron solution gauge field function) negative modes is rigorously proven. The same results hold for the Einstein-Yang-Mills black holes as well.

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arXiv1996

Computation of the winding number diffusion rate due to the cosmological sphaleron

A detailed quantitative analysis of the transition process mediated by a sphaleron type non-Abelian gauge field configuration in a static Einstein universe is carried out. By examining spectra of the fluctuation operators and applying the zeta function regularization scheme, a closed analytical expression for the transition rate at the one-loop level is derived. This is a unique example of an exact solution for a sphaleron model in $3+1$ spacetime dimensions.

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arXiv1994

Odd-Parity Negative Modes of Einstein-Yang-Mills Black Holes and Sphalerons

An analytical proof of the existence of negative modes in the odd--parity perturbation sector is given for all known non-abelian Einstein--Yang--Mills black holes. The significance of the normalizability condition in the functional stability analysis is emphasized. The role of the odd--parity negative modes in the sphaleron interpretation of the Bartnik--McKinnon solutions is discussed.

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arXiv1994

Einstein-Yang-Mills Sphalerons and Level Crossing

The fermion energy spectrum along paths which connect topologically distinct vacua in the Einstein-Yang-Mills theory passing through the gravitational sphaleron equilibrium solutions is investigated.

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arXiv1994

Einstein-Yang-Mills sphalerons and fermion number non-conservation

It is argued that the sphaleron solutions appearing in the Einstein-Yang-Mills theory are important in the transition processes at extremely high energies. Namely, when the energy exceeds the sphaleron mass, the existence of these solutions ensures constructive interference on the set of the overbarrier transition histories interpolating between distinct topological sectors of the theory. This has to lead to an enhancement of the transition rate and the related non-conservation of the fermion number.

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arXiv1994

Fermion number non-conservation and gravity

It is shown that in the Einstein-Yang-Mills (EYM) theory, as well as in the pure flat space Yang-Mills (YM) theory, there always exists an opportunity to pass over the potential barrier separating homotopically distinct vacuum sectors, because the barrier height may be arbitrarily small. However, at low energies all the overbarrier histories are suppressed by the destructive interference. In the pure YM theory the situation remains the same for any energies. In the EYM theory on the other hand, when the energy is large and exceeds the ground state EYM sphaleron mass, the constructive interference occurs instead. This means that in the extreme high energy limit the exponential suppression of the fermion number violation in pure YM theory is removed due to gravitational effects.

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