Analytic approach to confinement and monopoles in lattice SU (2)

We extend the approach of Banks, Myerson, and Kogut for the calculation of the Wilson loop in lattice U (1) to the non-abelian SU (2) group. The original degrees of freedom of the theory are integrated out, new degrees of freedom are introduced in several steps. The centre group enters automatically through the appearance of a field strength tensor , which takes on the values 0 or 1 only. It obeys a linear field equation with the loop current as source. This equation implies that is non vanishing on a two-dimensional surface bounded by the loop, and possibly on closed surfaces. The two-dimensional surfaces have a natural interpretation as strings moving in euclidean time. In four dimensions we recover the dual Abrikosov string of a type II superconductor, i.e. an electric string encircled by a magnetic current. In contrast to other types of monopoles found in the literature, the monopoles and the associated magnetic currents are present in every configuration. With some plausible, though not generally conclusive, arguments we are directly led to the area law for large loops. Received: 27 August 1999 / Revised version: 29 October 1999 / Published online: 21 December 1999     

Spherical symmetry and magnetic monopoles

I give a general, gauge-invariant, definition of spherical symmetry in a gauge theory. I show that if the fields are required to be non-singular at the origin, such symmetry can occur only for certain values of the magnetic charge. One consequence is the existence of stable monopoles which are not spherically symmetric.     

Finite-energy SU(3) monopoles

Classical SU(3) Yang-Mills-Higgs theory with the Higgs field in the adjoint representation is studies, when the SU(3) symmetry is broken down to U(3) and U(1)×U(1). Spherically symmetry equations of motion are solved for various boundary conditions. The finite-energy solutions correspond to magnetic monopoles and isopoles.     

A numerical study of SU(3) charge-two monopoles with minimal symmetry breaking

Charge-two SU(3) monopoles with minimal symmetry breaking can be generated via Nahm's equations. This paper investigates the detailed structure of such monopoles, through explicit calculation of the energy density, and the norm and discriminant of the Higgs field. Monopoles may be classified according to the maxima and minima of these quantities.     

Polynomial invariants for SU(2) monopoles

We present an explicit expression for the topological invariants associated to SU(2) monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding topological quantum field theory, and it turns out that they can be expressed in terms of Seiberg-Witten invariants. In this analysis we use recent exact results on the moduli space of vacua of the untwisted N = 1 and N = 2 supersymmetric counterparts of the topological quantum field theory under consideration, as well as on electric-magnetic duality for N = 2 supersymmetric gauge theories.     

SU(2) monopoles of charge 2

Using the methods of Hitchin, the moduli space of SU(2) monopoles of charge two is computed.     

Magnetic monopoles from a hidden magnetic symmetry

It is proposed that Magnetic Monopoles (MMs) could originate from a new U(1)_M symmetry. Such an abelian symmetry is assumed to be related to the conservation of a magnetic number M. This number is associated with massive MMs corresponding to an expected high scale breaking of the magnetic symmetry. The involved scales are approached and the properties of such MMs are investigated including their detection prospects.     

Anomalous baryon number non-conservation in the presence of SU(5) monopoles

It is shown that the effects related to the Adler-Bell-Jackiw anomaly give rise to strong baryon number non-conservation in the presence of magnetic monopoles in the SU(5) grand unified theory. The main assumption made is that, as long as distances of order 1 GeV^?1 from the monopole center are considered, the masses of light fermions u, d, s, e, μ can be neglected, while heavy fermions decouple. Two types of the SU(5) monopoles are studied, namely: (i) the fundamental monopole with a non-vanishing chromomagnetic charge, (ii) the minimal purely electromagnetic monopole. In both cases the processes like

$\text{p}\text{+}\text{monopole}\text{→}\text{e}{}^{\mathrm{+}}\text{+}\text{momopole}\text{+}\text{everything}$

are allowed. It is argued that the cross sections of these processes are of order 1 GeV^?2β^?2, at least for sufficiently low monopole-proton relative velocities β.     

SU(5) symmetry of spdfg interacting boson model

The extended interacting boson model with s-, p-, d-, f- and g-bosons included (spdfg IBM)is investigated. The algebraic structure including the generators, the Casimir operators of the groups at the SU(5) dynamical symmetry and the branching rules of the irreducible representation reductions along the group chain are obtained. The typical energy spectrum of the symmetry is given.     

Magnetic monopoles in SU(N) gauge theories

The potential $\text{A}\text{(}\text{r}\text{) ≡}\text{M}\text{(}\text{r}\text{?}\text{×}\text{n}\text{?}\text{)(r?}\text{r}\text{·}\text{n}\text{?}\text{)}{}^{\mathrm{?1}}$ is a static solution to the classical theory of non-abelian gauge fields coupled to a point magnetic source, for any matrix $\text{M}$ in the Lie algebra of the gauge group G. This solution is rotationally invariant if the eigenvalues of $\text{M}$ in the adjoint representation of G are quantized in half-integer units, but is stable to small perturbations only if all non-vanishing eigenvalues are $\text{±}\text{1}\text{2}$. In this paper, for the gauge groups G = SU(N), it is shown which sets of eigenvalues of $\text{M}$ are consistent with the group structure, which consistent sets are gauge inequivalent, and which consistent gauge inequivalent sets correspond to stable monopoles. It is found that there are N inequivalent stable monopoles, including the trivial case $\text{M}\text{=}\text{0}$. Equivalence here is with respect to non-singular gauge transformations—the symmetry transformations of the classical theory. Singular gauge transformations are, in contrast, not symmetries but they are nevertheless useful for classifying solutions and for relating the above concept of local stability to the global, or topological, stability associated with the Dirac strings. In this context, it is shown that there are N distinct topological classes of monopoles, with the group structure of the center $\text{Z}{}_{\mathrm{N}}\text{?Π}{}_1\text{(}\text{SU}\text{(N)/}\text{Z}{}_{\mathrm{N}}\text{)}$ of SU(N), that each class contains exactly one stable monopole, and that any other monopole in the same class has a strictly larger value of the magnetic charge magnitude $\text{tr}\text{M}{}^2$. This leads to an interesting physical picture of local stability as a consequence of the minimization of magnetic energy. The paper concludes with some comments on related topics: the empirical absence of magnetic charge, `t Hooft's calculation of magnetic energy, magnetic confinement, and spontaneously broken theories.     

SU(3) symmetry breaking for masses, magnetic moments and sizes of baryons

We use the SU(3) Skyrme model to investigate the effects of symmetry breaking imposed by different pseudoscalar meson masses on the structure of baryons. Specifically, we calculate their mass splittings, magnetic moments, charge radii, semileptonic decays as well as different strangeness contents of the proton. Since the Skyrme soliton is allowed to deform under the pressure of the symmetry breaking we find significant variations in baryon sizes with respect to strangeness.     

Magnetic moments ofb-quark baryons in broken SU(5) symmetry

The magnetic moments ofb-quark baryons within the framework of five quark models are derived. Also the transition magnetic moments of variousb-quark baryons are calculated.     

Radiative gauge symmetry breaking in supersymmetric flipped SU(5)

The radiative breaking of the SU(5)×U(1) symmetry in the flipped SU(5) model recently proposed by Antoniadis et al. is studied using renormalization group techniques. It is shown that gaugino masses can only be the dominant source of supersymmetry breaking at the Planck scale if the U(1) gaugino mass M₁ is at least 10 times larger than the SU(5) gaugino mass M₅. If M₁≅M₅ at the Planck scale, non-vanishing trilinear soft breaking terms (“A-terms”) are needed already at the Planck scale. In both cases consequences for the sparticle spectrum at the weak scale are discussed.     

SU(4) symmetry and hadron classification

We present here a quark model in SU(4) and classify hadrons. Weight diagrams are drawn. We give some mathematical aspects of SU(4) symmetry in the light of charmed quantum number.We are thankful to Prof. N. N.Raina for keen interest shown in our work and constant encouragement.     

Magnetic monopoles in SU(3) and SU(2) gauge theories without Higgs' scalars

We show that certain known singular solutions for pure SU(3) Yang-Mills theory carry magnetic charges with respect to both U(1) subgroups of SU(3). A topological characterisation in terms of monopoles is given to the SU(2) singular solutions of Wu and Yang.     

SU (4) × SU (4) symmetry breaking and its implications for SU (3) × SU (3) breaking

We investigate models where the SU (4) × SU (4) symmetry breaking Hamiltonian, $\text{H}$_SB, belongs to the (15, 15) and $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ representations, and show how they are equivalent to models of SU (3) × SU (3) breaking where $\text{H}$_SB belongs to a mixture of different representations. The results for the ππ scattering lengths in the (15, 15) model are outside the experimental limits, but the $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ model yields solutions with a wide range of values for the scattering lengths within the experimental bounds.     

Cylindrically and spherically symmetric monopoles in SU(3) gauge theory

We apply to the Atiyah-Ward ansätze a systematic procedure locating symmetric monopoles in SU(3) gauge theory broken to U(1) × U(1). In particular we recover the known spherically symmetric monopole as a limit of a cylindrically symmetric separated two monopole solution in SU(3). We also discuss the spherically symmetric monopole in SU(n). This latter is the only instance where we have properly shown the smoothness of the Higgs and gauge fields.