Complex structure of monopoles

Instanton techniques are applied to the classical monopole equations. The Prasad-Sommerfield monopole is rederived in a curious way, and new complex solutions are found, representing a distorted monopole     

Interacting monopoles

The Bogomolny equation for interacting monopoles of like charge in the case of vanishing Higgs mass is fulfilled by an asymptotic expansion in powers of the inverse monopole distance. Consequently, the monopoles exert no long range forces on each other. However, the expansion is not summable. The degrees of freedom of the multi-monopole system are discussed.     

On the construction of monopoles

We show that any self-dual SU (2) monopole may be constructed either by Ward's twistor method, or Nahm's use of the ADHM construction. The common factor in both approaches is an algebraic curve whose Jacobian is used to linearize the non-linear ordinary differential equations which arise in Nahm's method. We derive the non-singularity condition for the monopole in terms of this curve and apply the result to prove the regularity of axially symmetric solutions.     

Magnetic monopoles

These are notes of the first part of the lectures given at the JINR-ISU Baikal Summer School on Physics of Elementary Particles and Astrophysics (July 2010). I review classical monopole solutions of the SU(2) Yang-Mills-Higgs theory providing a pedagogical introduction into to the theory of non-Abelian monopoles both in the BPS limit and beyond of it. I briefly discuss monopole dynamics, the idea of the moduli space and some of the basic properties which are connected with the field theoretical aspects of these classical solutions.     

Magnetic monopoles

Summary Theoretical foundations for the existence of magnetic monopoles are given. Consequences extracted from cosmological and astrophysical considerations on the abundance of magnetic monopoles today are reviewed. The latest experimental results in the search for classical monopoles as well as for grand unified monopoles are summarized.

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Riassunto Si danno i fondamenti teorici per l'esistenza di monopoli magnétici. Si esaminano le conseguenze tratte da considerazioni cosmologiche e astrofisiche sull'abbondanza di monopoli magnetici attuale. Si riassumono i piú recenti risultati sperimentali sulla ricerca di monopoli classici e di quelli della grande unificazione.

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Резюме Приводятся теоретические обоснования сушствования магнитных монополей. Анализируются следствия из космологических и астрофизических рассмотрений, касающиеся распространенноси магнитных мононолей в настоящее время. Приводятся последние экспериментальные результаты по поискы классических монополей и монополей Великого Объединения.

     

Quaternionic monopoles

We present the simplest non-abelian version of Seiberg-Witten theory: Quaternionic monopoles. These monopoles are associated withSpin ^h (4)-structures on 4-manifolds and form finite-dimensional moduli spaces. On a Kähler surface the quaternionic monopole equations decouple and lead to the projective vortex equation for holomorphic pairs. This vortex equation comes from a moment map and gives rise to a new complex-geometric stability concept. The moduli spaces of quaternionic monopoles on Kähler surfaces have two closed subspaces, both naturally isomorphic with moduli spaces of canonically stable holomorphic pairs. These components intersect along a Donaldson instanton space and can be compactified with Seiberg-Witten moduli spaces. This should provide a link between the two corresponding theories.Partially supported by: AGE-Algebraic Geometry in Europe, contract No ERBCHRXCT940557 (BBW 93.0187), and by SNF, nr. 21-36111.92     

Colored magnetic monopoles

We extend Dirac's theory of magnetic monopoles to the case of non-Abelian color gauge groups. Exact classical solution is obtained by making use of the gauge-independent method of Yang-Mills field. The case of broken gauge symmetry is also briefly discussed.     

Colored monopoles on the lattice

Monopoles which carry both electro- and chromomagnetic charge are described by introducing new degrees of freedom into the hamiltonian form of SU(3)_color × U(1)_em lattice gauge theory. The monopoles we discuss exist as classical solutions in the SU(5) grand unified theory. The lattice theory allows us to describe the properties of these monopoles at low energies, where the color forces are strong. Our results are in agreement with a previous analysis by Coleman.     

Gravitationally bound monopoles

We construct monopole solutions in SU(2) Einstein-Yang-Mills-Higgs theory carrying magnetic charge n. For vanishing and small Higgs self-coupling, these multimonopole solutions are gravitationally bound. Their mass per unit charge is lower than the mass of the n = 1 monopole. For large Higgs self-coupling only a repulsive phase exists.     

Self-dual magnetic monopoles

The present status of self-dual monopoles is reviewed with a particular attention to a duality conjecture.Invited talk at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–21, 1981.     

Non-Abelian magnetic monopoles

It is shown that a general, irreducible, SU(n), Sp(n), SO(2n) monopole with maximal symmetry breaking is determined by its spectral data. For SU(n) with minimal symmetry breaking the spectral data is defined and also shown to determine the monopole.Research supported in part by NSF Grant 8120790     

Cosmological Kaluza-Klein monopoles

A solution of a pair of monopoles in 5D Kaluza-Klein theory without matter fields is given. The scale of the internal space is the same as that of the outer space. Its euclidean version is useful for calculating the wave function of the universe with monopoles.     

Quantization of superparametrized monopoles

Classical finite-energy solutions of the SU(2) Yang-Mills-Higgs system in four-dimensional space-time are embedded in the supersymmetric extension of the theory. Finite supertranslations are constructed and are used to obtain a family of solutions to the supersymmetric field equations, parametrized by fermionic Majorana spinor parameters. The quantum theory around arbitrary classical solutions, parametrized by arbitrary bosonic (global and local) as well as fermionic (global) parameters, is constructed and discussed.     

Unambiguous detection of monopoles

Summary The fission of a vortex line along the trajectory of a monopole in a superconducting medium is an unambiguous signature of a monopole. The numbern of the (stable) daughter vortices determines the monopole strengthg withg=2nφ/4π where ϕ₀=2.07·10⁻⁷ G cm².

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Riassunto La fissione di una linea di vortice lungo la traiettoria di un monopolo in un mezzo superconduttore è indice sicuro della segnatura di un monopolo. Il numeron di vortici figli (stabili) determina la forza del monopolog cong=nϕ₀/4π, dove ϕ₀=2.07·10⁻⁷ G cm².

     

Dynamics of periodic monopoles

BPS monopoles which are periodic in one of the spatial directions correspond, via a generalized Nahm transform, to solutions of the Hitchin equations on a cylinder. A one-parameter family of solutions of these equations, representing a geodesic in the 2-monopole moduli space, is constructed numerically. It corresponds to a slow-motion dynamical evolution, in which two parallel monopole chains collide and scatter at right angles.