Related papers: A gluing construction for periodic monopoles
There exist several types of monopole - like topological defects in Electroweak theory. We investigate properties of these objects using lattice numerical methods. The intimate connection between them and the dynamics of the theory is…
Extended Abelian monopoles are investigated in SU(2) lattice gauge theory in three dimensions. Monopoles are computed by Abelian projection in several gauges, including the maximal Abelian gauge. The number $N_m$ of extended monopoles in a…
We study the problem of desingularizing coassociative conical singularities via gluing, allowing for topological and analytic obstructions, and discuss applications. This extends the author's earlier work on the unobstructed case. We…
A model of monopolium is constructed based on an electromagnetic dual formulation of Zwanziger and lattice gauge theory. To cope with the strong coupling nature of the magnetic charge, for which the monopole is confined, $ U(1) $ lattice…
This is the third installment in our series of articles (dg-ga/9712005, dg-ga/9710032) on the application of the PU(2) monopole equations to prove Witten's conjecture (hep-th/9411102) concerning the relation between the Donaldson and…
We present measurements of various geometrical characteristics of monopole clusters in SU(2) lattice gauge theory. The maximal Abelian projection is employed and both infinite, or percolating cluster and finite clusters are considered. In…
We consider monopoles with singularities of Dirac type on quasiregular Sasakian three-folds fibering over a compact Riemann surface $\Sigma$, for example the Hopf fibration $S^3\longrightarrow S^2$. We show that these correspond to…
The monopole confinement mechanism in the abelian projection of lattice gluodynamics is reviewed. The main topics are: the abelian projection on the lattice and in the continuum, a numerical study of the abelian monopoles in the lattice…
We produce many new complete, constant Q-curvature metrics on finitely punctured spheres by gluing together known examples. In our construction we truncate one end of each summand and glue the two summands together "end-to-end," where we've…
We prove the "Gluing Conjecture" on the spectral side of the categorical geometric Langlands correspondence. The key tool is the structure of crystal on the category of singularities, which allows to reduce the conjecture to the question of…
Magnetic singularities, also known as magnetic monopoles or Bloch points, represent intriguingphenomena in nanomagnetism. We show that a pair of coupled Bloch points may appear as alocalized, stable state in cubic chiral magnets. Detailed…
We review the method of blocking of topological defects from continuum used as a non--perturbative tool to construct effective actions for these defects. The actions are formulated in the continuum limit while the couplings of these actions…
We characterize commutative idempotent involutive residuated lattices as disjoint unions of Boolean algebras arranged over a distributive lattice. We use this description to introduce a new construction, called gluing, that allows us to…
Using the renormalization group motivated smoothing technique, the large scale structure of lattice configurations at finite temperature is characterized in terms of Abelian monopoles identified in the maximally Abelian, the Laplacian…
We introduce a gauge invariant definition of a monopole on the lattice. The construction is based on the observation that for each Wilson loop there exists an extra U(1) group which leaves the loop invariant. Since the lattice formulation…
We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or appropriate subreducts, of the resulting structure. Starting from the 1-sum construction…
We construct solutions for the fractional Yamabe problem that are singular at a prescribed number of isolated points. This seems to be the first time that a gluing method is successfully applied to a non-local problem. The main step is an…
The behavior of a massive scalar particle on the spacetime surrounding a monopole is studied from a quantum mechanical point of view. All the boundary conditions necessary to turn into self-adjoint the spatial portion of the wave operator…
The present theory is based on the assumption that at the very small (Planck scale) distances our space-time is discrete, and this discreteness influences on the Planck scale physics. Considering our (3+1)-dimensional space-time as a…
We study the relation between the flux of a center vortex obtained from the center vortex model and the flux formed between monopoles obtained from the Abelian gauge fixing method. Motivated by the Monte Carlo simulations which have shown…