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The 't Hooft-Polyakov monopole solution in Yang-Mills theory is given new physical interpretation in the geometric theory of defects. It describes solids with continuous distribution of dislocations and disclinations. The corresponding densities of Burgers and Frank vectors are computed. It means that the 't Hooft-Polyakov monopole can be seen, probably, in solids., Comment: 10 pages, 2 figures

We consider 't Hooft-Polyakov monopole (TPM) as a topological soliton in the 5-dimensional (5D) theory of gauge-Higgs unification. This scenario provides a very natural framework to incorporate the TPM, since the adjoint scalar is builtin as the extra-space component of higher dimensional gauge field. In the process of the analysis, we realize that the condition to be satisfied by the Bogomolny-Prasad-Sommerfield (BPS) state of TPM, the BPS monopole, is equivalent to an (anti-)self-dual condition for the higher dimensional gauge field. This observation, in turn, suggests the presence of instanton-like topological soliton living in the 4D space (including the extra dimension), instead of the 4D space-time in the case of ordinary instanton, say "space-like instanton" with finite energy, instead of finite action. We construct the field configuration for the space-like instanton and calculate its mass, handled by the compactification scale. Next we discuss the BPS monopole, as an anti-self-dual gauge field. We start by constructing a hedgehog-type solution as what is obtained by a local gauge transformation from a trivial vacuum. We also argue in some detail that the relation between these two types of topological solitons becomes manifest through the unified description by use of the ansatz adopted by 't Hooft., 15 pages, no figure, published version at JPSJ

The Lorentz invariance is broken for the non-Abelian monopoles. Here we will consider the case of the 't Hooft–Polyakov monopole and show that the Lorentz invariance of its field will be restored using Dirac quantization.

In this paper, making use of the 't Hooft-Polyakov-Julia-Zee ansatz for the SU(2) Yang-Mills-Higgs gauge field theory, we present the straightforward generalization of the Bogomoln'yi equations and its several consequences. Particularly, this is shown that this idea is able to generate new types of non-abelian both dyons and magnetic monopoles and, moreover, that within the new model the scalar field can be described through the Coulomb potential, whereas, up to a constant, the non-abelian gauge field becomes the Wu-Yang monopole., 12 pages

Recently we have reported on the existence of finite energy SU(2) Yang-Mills-Higgs particle of one-half topological charge. In this paper, we show that this one-half monopole can co-exist with a ’t Hooft-Polyakov monopole. The magnetic charge of the one-half monopole is −12 while the magnetic charge of the ’t Hooft-Polyakov monopole is positive unity. However the net magnetic charge of the configuration is zero due to the presence of a semi-infinite Dirac string along the positive z-axis that carries the magnetic monopole charge of another −12. The solution possesses gauge potentials that are singular along the z-axis, elsewhere they are regular. This monopole configuration possesses finite total energy and magnetic dipole moment. The total energy is found to increase with the strength of the Higgs field self-coupling constant λ. However the dipole separation and the magnetic dipole moment decrease with λ. This solution is non-BPS even in the BPS limit when the Higgs self-coupling constant vanishes.

We construct BPS solutions representing M2-M5 bound state in the ABJM action explicitly. They include the funnel type solutions and 't Hooft Polyakov monopole solutions. Furthermore, we give a one to one correspondence between the solutions of the BPS equation and the ones of an extended Nahm equation which includes the Nahm equation. This enables us to construct infinitely many conserved quantities from the Lax form of the Nahm equation.

The mass and interactions of a quantum 't Hooft-Polyakov monopole are measured nonperturbatively using correlation functions in lattice Monte Carlo simulations. A method of measuring the form factors for interactions between the monopole and fundamental particles, such as the photon, is demonstrated. These quantities are potentially of experimental relevance in searches for magnetic monopoles., 11 pages, 6 figures; v2: minor changes to introduction and conclusions, published in PRD

We present a systematic approach to the linearised Yang-Mills-Higgs equations in the background of a 't Hooft-Polyakov monopole and use it to unify and extend previous studies of their spectral properties. We show that a quaternionic formulation allows for a compact and efficient treatment of the linearised equations in the BPS limit of vanishing Higgs self-coupling, and use it to study both scattering and bound states. We focus on the sector of vanishing generalised angular momentum and analyse it numerically, putting zero-energy bound states, Coulomb bound states and infinitely many Feshbach resonances into a coherent picture. We also consider the linearised Yang-Mills-Higgs equations with non-vanishing Higgs self-coupling and confirm the occurrence of Feshbach resonances in this situation., 33 pages, 7 figures

We obtain the equations for the quantum fluctuations of gauge and Higgs fields in the background of a 't Hooft-Polyakov monopole. The integration of these equations at frequency zero provides a check for the stability of the classical solution according to the Jacobi criterion. The numerical analysis shows that the monopole is indeed stable against spherical and non-spherical fluctuations.

We study a simple quantum mechanical model of a spinning particle moving on a sphere in the presence of a magnetic field. The system has two ground states. As the magnetic field is varied, the ground states mix through a non-Abelian Berry phase. We show that this Berry phase is the path ordered exponential of the smooth $SU(2)$ 't Hooft--Polyakov monopole. We further show that, by adjusting a potential on the sphere, the monopole becomes a Bogomol'nyi-Prasad-Sommerfield monopole and obeys the Bogomol'nyi equations.

We exploit the 't Hooft-Polyakov monopole to define closed algebra of the quantum field operators and the BRST charge $Q_{BRST}$. In the first-class configuration of the Dirac quantization, by including the $Q_{BRST}$-exact gauge fixing term and the Faddeev-Popov ghost term, we find the BRST invariant Hamiltonian to investigate the de Rham-type cohomology group structure for the monopole system. The Bogomol'nyi bound is also discussed in terms of the first-class topological charge defined on the extended internal 2-sphere., Comment: 8 pages

Properties of the 't Hooft-Polyakov monopole in pure SU(2) gauge theory are studied. This is of interest for an implementation of the dual superconductor hypothesis of confinement.

The quantum mechanical mass of 't Hooft-Polyakov monopoles in the four-dimensional Georgi-Glashow is calculated non-perturbatively using lattice Monte Carlo simulations. This is done by imposing twisted boundary conditions that ensure there is one unit of magnetic charge on the lattice, and measuring the free energy difference between this ensemble and the vacuum. In the weak-coupling limit, the results can be used to determine the quantum correction to the classical mass, once renormalisation of couplings is taken properly into account. The methods can also be used to study the masses at strong coupling, i.e., near the critical point, where there are hints of a possible electric-magnetic duality., 17 pages, 4 figures. Typos corrected, one reference added

In this article, we carry out the Hamiltonization in the axial gauge, of the t'Hooft-Polyakov monopole field outside the localized region, which represents the monopole's core. One feature of the treatment here, is using the Higgs vacuum condition as both strong and weak equation instead of using it in the degree of freedom reduction.

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, $E_n=\omega_n-i\gamma_n$, satisfying the outgoing radiation condition. For $n\to\infty$, their frequencies $\omega_n$ approach the mass of the vector boson, $M_W$, while their lifetimes $1/\gamma_n$ 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 $t^{-5/6}$., Comment: 4 pages

We investigate several properties of Ginsparg-Wilson fermion on fuzzy 2-sphere. We first examine chiral anomaly up to the second order of the gauge field and show that it is indeed reduced to the correct form of the Chern character in the commutative limit. Next we study topologically non-trivial gauge configurations and their topological charges. We investigate 't Hooft-Polyakov monopole type configuration on fuzzy 2-sphere and show that it has the correct commutative limit. We also consider more general configurations in our formulation., Comment: Latex 32 pages, references added, typo corrected, the final version to appear in Nucl.Phys.B

We examine whether the analysis of quantum corrections for the kink soliton carries over to the 't Hooft-Polyakov monopole. For the kink, it is central that the quantum fluctuations are eigenmodes of a Hermitian operator. For the monopole, we show the analogous operator is not Hermitian. This property raises some questions about the quantization procedure for a 't Hooft-Polyakov monopole., 5 pages, LaTeX

The paper presents a particle physicists’ interpretation of the mathematical abstract concept of a five dimensional empty set as the source of dark energy and dark matter. It turns out that the simplest alternative physical interpretation at least from the view point of the GUT unification of fundamental interaction is the theoretically well established but experimentally never found yet ‘t Hooft-Polyakov magnetic giant monopole with the predicted huge mass of ten to the power of 16 Gev. In fact it will be shown here using exact renormalization equations that running the preceding energy logarithmically leads to a prediction of the ordinary and the total dark energy density of the cosmos in complete agreement with our earlier result E(O) = mc2/22 and E(D) = mc2(21/22) based on the afore mentioned set theoretical concepts as well as with all the relatively recent cosmological measurements. The decisive steps in the present derivation consists of two realizations. First and to our deepest surprise and delight, E =γmc2 = mc2 is actually a unification formula uniting classical, relativistic and quantum mechanics where γ= 1 corresponds to a 100% energy density. Second and also not expectedly, the logarithmic running of ‘t Hooft-Polyakov’s monopole energy leads to a reduction factor γ= 1/λwhere λ=1/2 ln (M(monopole))/(m(electron))=22.18033989, in full agreement with our previous results using entirely different approaches. Finally the results are validated using ‘t Hooft’s dimensional regularization D = 4 ∈ by setting = 2∅^5 where ∅^5 is Hardy’s quantum entanglement and φ=2/ √5+1.

A realization of E_{n+1} monopoles in string theory is given. The NS five brane stuck to an Orientifold eight plane is identified as the 't Hooft Polyakov monopole. Correspondingly, the moduli space of many such NS branes is identified with the moduli space of SU(2) monopoles. These monopoles transform in the spinor representation of an SO(2n) gauge group when n D8 branes are stacked upon the orientifold plane. This leads to a realization of E_{n+1} monopole moduli spaces. Charge conservation leads to a dynamical effect which does not allow the NS branes to leave the orientifold plane. This suggests that the monopole moduli space is smooth for n8 obeys a similar condition. Using a chain of dualities, we also connect our system to an Heterotic background with Kaluza-Klein monopoles., 26 pages, 3 figures

We study the interaction of the t’Hooft–Polyakov monopole with weak external fields. The basic idea is to treat the excitation of a monopole zero mode as the monopole displacement. The excitation is found perturbatively. We consider the interaction of the t’Hooft–Polyakov monopole with an external uniform magnetic field.

Two solutions are given for the complete 't Hooft-Polyakov monopole equations. One of these satisfies the boundary conditions at infinity, while the other satisfies the boundary conditions atr=0. Even if the two solutions do not match together for intermediate values ofr, they are, however, rigorous for the boundary conditions taken separately.

It is shown that the Georgi-Glashow Lagrangian is invariant (and therefore the ’t Hooft-Polyakov monopole solutions are covariant) under conformal transformations. The same procedure is not suitable for Dirac-Maxwell theory because of nonstandard variational principle. The conformal covariance of this theory is directly proved.

A virial theorem for solitons derived by Friedberg, Lee and Sirlin is used to reduce a system of second order equations to an equivalent first order set. It is shown that this theorem, when used in conjunction with our earlier observation that soliton-like solutions lie on the separatrix, helps in obtaining soliton-like solutions of theories involving coupled fields. The method is applied to a system of equations studied extensively by Rajaraman. The ’t-Hooft-Polyakov monopole equations are then studied and we obtain the well-known monopole solutions in the Prasad-Sommerfeld limit (λ=0); for the case λ≠0, we succeed in obtaining a non-trivial algebraic constraint between the fields of the theory.

The study of extended solutions of classical nonlinear field equations recently aroused a wide interest because of its relevance in problems of hadron physics., Facultad de Ciencias Exactas

A perturbative classical monopole solution for the SO(3) gauge theory is constructed in the limit of small but non-vanishing Higgs potential. This corresponds to the limit μ 2 2M W 2 = λ ⪡ 1 , where μ equals the mass of the scalar particle and MW equals the mass of the intermediate vector particles. The monopole solution and mass are found to involve non-analytic functions of λ: γ and λ ln λ. The monopole mass Mm is calculated to order μ 2 M W as M m = 4π e 2 M w 1+ 1 2 μ M w + 1 2 μ 2 M 2 w ln μ M w +0.7071 μ 2 M 2 w .

It is shown that the ansatz for the asymptotic (r → ∞) gauge fields used by ’t Hooft in the study of monopoles in SO(3) electroweak theory is not unique.

The authors consider the dynamics of a point-like SU(2) isocharge which creates a weak disturbance in the field of a 't Hooft-Polyakov monopole. A local, gauge-invariant measure of the isocharge is introduced and its evolution is computed for various motions, to leading order in a small parameter epsilon , where epsilon measures the weakness of the disturbance. In contrast, to ordinary electromagnetic charge, the gauge-invariant isocharge need not remain constant, but rather undergoes a net change, for certain motions, as a result of its interaction with the monopole.

TheO(5)×U(1) electroweak gauge theory with two particle generations of quarks and leptons is considered. With spontaneous symmetry breaking down to theO(3) level, the 't Hooft-PolyakovSO(3) monopole theory along with its triplet of scalar fields is reproduced and developed to the extent necessary to establish the results. It is shown that the existence of the monopole triggers the Cabibbo rotation ofd ands along with theν e andν µ flavors, which in turn results in the neutrino oscillations. The neutrino oscillation angle turns out to be the Cabibbo angle. Using the experimental data of Bakeret al., an upper limit is set on Δm 2≤1.3 eV2 (Δm 2≡ µ 2 −m 2 ). Furthermore, it is exactly the Cabibbo angle in which the isovector $$\bar \phi$$ has to be rotated so as to spontaneously break the symmetry down to theO(3) level, together with, on theSO(3) sector, to theU(1) level. It turns out that the Weinberg angle is twice the Cabibbo angle, a result already noted elsewhere.

By means of a “lagrangian” with values in the Lie algebra of some arbitrary Lie group we introduce a non-abelian path integral. For such generalised quantum mechanics we derive a non-abelian Schrodinger equation for the case of a particle in the 't Hooft-Polyakov monopole field.

The zero energy eigenvalue problem for quantum fluctuations about the 't Hooft-Polyakov monopole solution is solved explicitly in the Prasad-Sommerfield limit, by exploiting the formal similarity with self-dual euclidean field configurations. The relevance of the results to the spin of the quantized monopole is examined.

This paper presents an exact solution of the Dirac equation for an $I=\frac{1}{2}$ fermion in the field of a 't Hooft-Polyakov magnetic monopole (in the Prasad-Sommerfield limit), which is analytic at $\mathcal{r}=0$. Helicity conservation restricts the $J=0$ $S$ matrix to be pure charge exchange. Because of the long-range interaction, the scattering amplitude is enhanced at long wavelengths $\ensuremath{\lambda}\ensuremath{\gg}\frac{1}{M}$ (the monopole structure size). The relevance of the present results for the question of proton decay catalysis is briefly discussed.

We present an exact solution to the nonlinear field equations which describe a classical excitation possessing magnetic and electric charge. This solution has finite energy and exhibits explicitly those properties which have previously been found by numerical analysis.

An isodoublet of fermions with unequal masses in the field of a 't Hooft-Polyakov monopole is considered. Charge-exchange and helicity-flip cross sections are derived for J = 0 in the limit (E/sub f/,m/sub f/)/M/sub GUT/..-->..0 and e/sup 2/..-->..0. The relevance of our results for the Rubakov-Callan effect is discussed.

We present regular solutions for a brane world scenario in the form of a 't Hooft-Polyakov monopole living in the three-dimensional spherical symmetric transverse space of a seven-dimensional spacetime. In contrast to the cases of a domain-wall in five dimensions and a string in six dimensions, there exist gravity-localizing solutions for both signs of the bulk cosmological constant. A detailed discussion of the parameter space that leads to localization of gravity is given. A point-like monopole limit is discussed., Comment: 29 pages, 17 figures

The fields near a slowly accelerating 't Hooft-Polyakov monopole in the Prasad-Sommerfield limit are obtained.