Narrow Results

The formalism of space–time dependent Lagrangians developed in Ref. 1 is applied to the sine-Gordon and massive Thirring models. It is shown that the well-known equivalence of these models (in the context of weak–strong duality) can be understood in this approach from the same considerations as described in Ref. 1 for electromagnetic duality. A further new result is that all these can naturally be linked to the fact that the holographic principle has analogues at length scales much larger than quantum gravity. There is also the possibility of noncommuting coordinates residing on the boundaries.

We give a formulation unifying the discussion of the spherical harmonics and the monopole harmonics. As a demonstration of the potency of this approach, we exhibit via this method a symmetry of the exchange of the quantum numbers m and q in the monopole harmonics.

Using the technique of spectral decomposition, we investigated the late-time tails of massless and massive coupled scalar fields in the background of a black hole with a global monopole. We found that due to the existence of the coupling between the scalar and gravitational fields, the massless scalar field decay faster at timelike infinity i₊, and so does the massive one in the intermediate late time. But the asymptotically late-time tail for the massive scalar field is not affected and its decay rate is still t^-5/6.

The nonrelativistic scattering of charged particles by non-quantized Dirac's monopole is explored. It is shown that the singular Dirac "string" should be observed in the quantum scattering experiment, if the Dirac quantization condition is discarded.

The D+D → ⁴He reaction can be one of the methods to count the magnetic monopole. In order to prove this, the mechanism of bound state of nucleons and monopole system is clarified. We calculated bound state of nucleon-monopole system by using the Jacobi-coordinate bases antisymmetrized molecular dynamics (or JAMD) method. This calculation is done to show the efficiency of JAMD as a first step of main subject. The binding energy of neutron and proton in the magnetic monopole field is calculated. Our results are compared with those of analytical solution.

We consider wormhole solutions in five-dimensional Kaluza–Klein gravity in the presence of a massless ghost four-dimensional scalar field. The system possesses two types of topological nontriviality connected with the presence of the scalar field and of a magnetic charge. Mathematically, the presence of the charge appears in the fact that the S³ part of a spacetime metric is the Hopf bundle S³ →S² with fiber S¹. We show that the fifth dimension spanned on the sphere S¹ is compactified in the sense that asymptotically, at large distances from the throat, the size of S¹ is equal to some constant, the value of which can be chosen to lie, say, in the Planck region. Then, from the four-dimensional point of view, such a wormhole contains a radial magnetic (monopole) field, and an asymptotic four-dimensional observer sees a wormhole with the compactified fifth dimension.

Axion electrodynamics is deduced from the local duality invariant electrodynamics (LDIE) with a new perspective on both formalism and the physical interpretation. First, the delicate issue of duality rotation symmetry in the Maxwell action is critically reviewed and the generalized Maxwell field equations invariant under local duality rotation are derived. In the alternative approach, a generalization is made to Sudbery’s pseudo-vector action such that it is local duality invariant. Variational principle is used to derive the Euler–Lagrange equations of motion. The gauge potential for local duality rotation, termed duroton, under the assumption that it is a gradient of the axion field leads to the dual symmetric axion electrodynamics. The absence of the magnetic monopole in Maxwell equations motivates to impose a natural condition to deduce the standard axion electrodynamics. The present derivation offers the possibility for new physical interpretation of the axions and the monopoles.

Using a one-loop renormalization group improvement for the effective potential in the Higgs model of electrodynamics with electrically and magnetically charged scalar fields, we argue for the existence of a triple (critical) point in the phase diagram (), where λ_run is the renormalized running self-interaction constant of the Higgs scalar monopoles and g_run is their running magnetic charge. This triple point is a boundary point of three first-order phase transitions in the dual sector of the Higgs scalar electrodynamics: The "Coulomb" and two confinement phases meet together at this critical point. Considering the arguments for the one-loop approximation validity in the region of parameters around the triple point A we have obtained the following triple point values of the running couplings: , which are independent of the electric charge influence and two-loop corrections to with high accuracy of deviations. At the triple point the mass of monopoles is equal to zero. The corresponding critical value of the electric fine structure constant turns out to be by the Dirac relation. This value is close to the , which in a U(1) lattice gauge theory corresponds to the phase transition between the "Coulomb" and confinement phases. In our theory for α ≥ α_crit there are two phases for the confinement of the electrically charged particles. The results of the present paper are very encouraging for the antigrand unification theory which was developed previously as a realistic alternative to SUSY GUT's. The paper is also devoted to the discussion of this problem.

We calculate the energy radiated by a uniformly moving charged scalar particle in the spacetime of a point-like global monopole, for small solid angle deficit. We show that this energy is proportional to the cube of the velocity of the particle and to the cube of the Lorenz factor, in the non-relativistic and ultra-relativistic cases, respectively. We also determine the energy shifts of a hydrogen atom placed in the background spacetime of a cosmic string and we discuss the possibility that these shifts could provide a means of probing for the presence of this topological defect in the Universe.

We study an effective theory of QCD in which the fundamental variables are dual magnetic potentials coupled to the monopole field. Dual dynamics are then used to explain the properties of QCD vacuum at zero temperature as well as at finite temperatures. At zero temperature, the color confinement is realized through the dynamical breaking of magnetic symmetry, which leads to the magnetic condensation of QCD vacuum. The flux tube structure of SU(2) QCD vacuum is investigated by solving the field equations in the low energy regimes of the theory, which guarantees dual superconducting nature of the QCD vacuum. The QCD phase transition at finite temperature is studied by the functional diagrammatic evaluation of the effective potential on the one-loop level. We then obtained analytical expressions for the vacuum expectation value of the condensed monopoles as well as the masses of glueballs from the temperature dependent effective potential. These nonperturbative parameters are also evaluated numerically and used to determine the critical temperature of the QCD phase transition. Finally, it is shown that near the critical temperature (T_c≃0.195 GeV), continuous reduction of vacuum expectation value (VEV) of the condensed monopoles caused the disappearance of vector and scalar glueball masses, which brings a second order phase transition in pure SU(2) gauge QCD.

We would like to present some exact SU(2) Yang–Mills–Higgs monopole solutions of half-integer topological charge. These solutions can be just an isolated half-monopole or a multimonopole with topological magnetic charge ½m where m is a natural number. These static monopole solutions satisfy the first order Bogomol'nyi equations. The axially symmetric one-half monopole gauge potentials possess a Dirac-like string singularity along the negative z-axis. The multimonopole gauge potentials are also singular along the z-axis and possess only mirror symmetries.

Recently, we have reported on the existence of some monopoles, multimonopole, and antimonopoles configurations. In this paper we would like to present more monopoles, multimonopole, and antimonopoles configurations of the magnetic ansatz of Ref. 9 when the parameters p and b of the solutions takes different serial values. These exact solutions are a different kind of BPS solution. They satisfy the first order Bogomol'nyi equation but possess infinite energy. They can have radial, axial, or rotational symmetry about the z-axis. We classified these serial solutions as (i) the multimonopole at the origin; (ii) the finitely separated 1-monopoles; (iii) the screening solutions of multimonopole and (iv) the axially symmetric monopole solutions. We also give a construction of their anticonfigurations with all the magnetic charges of poles in the configurations reversed. Half-integer topological magnetic charge multimonopole also exist in some of these series of solutions.

The property and gravitational field of global monopole of tachyon are investigated in a four-dimensional static space–time. We give an exact solution of the tachyon field in the flat space–time background. Using the linearized approximation of gravity, we get the approximate solution of the metric. We also solve analytically the coupled Einstein and tachyon field equations which is beyond the linearized approximation to determine the gravitational properties of the monopole solution. We find that the metric of tachyon monopole represents an asymptotically AdS space–time with a small effective mass at the origin. We show that this relatively tiny mass is actually negative, as it is in the case of ordinary scalar field.

The quantum Yang–Mills theory, describing a system of fields with nondual (chromoelectric g) and dual (chromomagnetic ) charges and revealing the generalized dual symmetry, is developed by analogy with the Zwanziger formalism in QED. The renormalization group equations (RGE's) for pure non-Abelian theories are analyzed for both constants, α = g²/4π and . The pure gauge theory is investigated as an example. We consider not only monopoles, but also dyons. The behavior of the total SU(3) β-function is investigated in the whole region of α≡α_s: 0≤α < ∞. It is shown that this β-function is antisymmetric under the interchange α ↔ 1/α and is given by the well-known perturbative expansion not only for α≪1, but also for α≫1. Using an idea of the Maximal Abelian Projection by 't Hooft, we have considered the formation of strings — the ANO flux tubes — in the Higgs model of scalar monopole (or dyon) fields. In this model we have constructed the behavior of the β-function in the vicinity of the point α = 1, where it acquires a zero value. Considering the phase transition points at α≈0.4 and α≈2.5, we give the explanation of the freezing of α_s. The evolution of with energy scale μ and the behavior of V_eff(μ) are investigated for both, perturbative and nonperturbative regions of QCD. It was shown that the effective potential has a minimum, ensured by the dual sector of QCD. The gluon condensate , corresponding to this minimum, is predicted: , in agreement with the well-known results.

In this paper we suggest a new model of preons–dyons making composite quark–leptons and bosons, described by the supersymmetric string-inspired flipped gauge group of symmetry. This approach predicts the possible extension of the Standard Model to the family replicated gauge group model of type G^N_fam, where N_fam is the number of families and G is the symmetry group: G = SMG, SU(5), SO(10), E₆, etc. Here E₆ and are nondual and dual sectors of theory with hyperelectric g and hypermagnetic charges, respectively. Starting with an idea that the most realistic model leading to the unification of all fundamental interactions (including gravity) is the "heterotic" string-derived flipped model, we have assumed that at high energies μ > 10¹⁶GeV there exists the following chain of the flipped models:

We present new classical generalized Jacobi elliptic one monopole–antimonopole pair (MAP) solutions of the SU(2) Yang–Mills–Higgs theory with the Higgs field in the adjoint representation. These generalized 1-MAP solutions are solved with θ-winding number m = 1 and ϕ-winding number n = 1, 2, 3,…,6. Similar to the generalized Jacobi elliptic one monopole solutions, these generalized 1-MAP solutions are solved by generalizing the large distance behavior of the solutions to the Jacobi elliptic functions and solving the second order equations of motion numerically when the Higgs potential is vanishing (λ = 0) and nonvanishing (λ = 1). These generalized 1-MAP solutions possess total energies that are comparable to the total energy of the 1-MAP solution with winding number m = 1. However these total energies are significantly lower than the total energy of the 1-MAP solution with winding number m = 2. All these new generalized solutions are regular numerical finite energy non-BPS solutions of the Yang–Mills–Higgs field theory.

We performed the Cho decomposition of the SU(2) Yang–Mills–Higgs gauge potentials of the finite energy (1) one-half monopole solution and (2) the one and a half monopoles solution into Abelian and non-Abelian components. We found that the semi-infinite string singularity in the gauge potentials is a contribution from the Higgs field of the one-half monopole in both of the solutions. The non-Abelian components of the gauge potentials are able to remove the point singularity of the Abelian components of the 't Hooft–Polyakov monopole but not the string singularity of the one-half monopole which is topological in nature. Hence the total energy of a one monopole is infinite in the Maxwell electromagnetic theory but the total energy of a one-half monopole is finite. By analyzing the magnetic fields and the gauge covariant derivatives of the Higgs field, we are able to conclude that both the one-half integer monopoles solutions are indeed non-BPS even in the limit of vanishing Higgs self-coupling constant.

Under the assumption of the Abelian dominance in QCD, we show that chiral condensate is locally present around a QCD monopole. The appearance of the chiral condensate around a GUT monopole was shown in the previous analysis of the Rubakov effect. We apply a similar analysis to the QCD monopole. It follows that the condensation of the monopole carrying the chiral condensate leads to the chiral symmetry breaking as well as quark confinement. To realize the result explicitly, we present a phenomenological linear sigma model coupled with the monopoles, in which the monopole condensation causes the chiral symmetry breaking as well as confinement. The monopoles are assumed to be described by a model of dual superconductor. Because the monopoles couple with mesons, we point out the presence of an observable color singlet monopole coupled with the mesons.

Under the assumption of Abelian dominance in QCD, we have shown that chiral condensate is locally present around each QCD monopole. The essence is that either charge or chirality of a quark is not conserved, when the low energy massless quark collides with QCD monopole. In reality, the charge is conserved so that the chirality is not conserved. Reviewing the presence of the local chiral condensate, we show by using chiral anomaly that chiral nonsymmetric quark pair production takes place when a color charge is putted in a vacuum with monopole condensation, while chiral symmetric pair production takes place in a vacuum with no monopole condensation. Our results strongly indicate that the chiral symmetry is broken by the monopole condensation.

After Dirac introduced the monopole, topological objects have played increasingly important roles in physics. In this review we discuss the role of the knot, the most sophisticated topological object in physics, and related topological objects in various areas in physics. In particular, we discuss how the knots appear in Maxwell’s theory, Skyrme theory, and multicomponent condensed matter physics.