Zero Modes of Rotationally Symmetric Generalized Vortices and Vortex Scattering

Zero modes of rotationally symmetric vortices in a hierarchy of generalized Abelian Higgs models are studied. Under the finite-energy and the smoothness condition, it is shown, that in all models, $n$ self-dual vortices superimposed at the origin have $2n$ modes. The relevance of these modes for vortex scattering is discussed, first in the context of the slow-motion approximation. Then a corresponding Cauchy problem for an all head-on collision of $n$ vortices is formulated. It is shown that the solution of this Cauchy problem has a $\frac{\pi}{n}$ symmetry.Comment: 12 pages. late

The euclidean propagator in a model with two non-equivalent instantons

We consider in detail how the quantum-mechanical tunneling phenomenon occurs in a well-behaved octic potential. Our main tool will be the euclidean propagator just evaluated between two minima of the potential at issue. For such a purpose we resort to the standard semiclassical approximation which takes into account the fluctuations over the instantons, i.e. the finite-action solutions of the euclidean equation of motion. As regards the one-instanton approach, the functional determinant associated with the so-called stability equation is analyzed in terms of the asymptotic behaviour of the zero-mode. The conventional ratio of determinants takes as reference the harmonic oscillator whose frequency is the average of the two different frequencies derived from the minima of the potential involved in the computation. The second instanton of the model is studied in a similar way. The physical effects of the multi-instanton configurations are included in this context by means of the alternate dilute-gas approximation where the two instantons participate to provide us with the final expression of the propagator.Comment: RevTex, 13 page

Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation

We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.Comment: 4 pages, 4 figures, typos correcte

Fermionic determinant for dyons and instantons with nontrivial holonomy

We calculate exactly the functional determinant for fermions in fundamental representation of SU(2) in the background of periodic instanton with non-trivial value of the Polyakov line at spatial infinity. The determinant depends on the value of the holonomy v, the temperature, and the parameter r_12, which at large values can be treated as separation between the Bogomolny--Prasad--Sommerfeld monopoles (or dyons) which constitute the periodic instanton. We find a compact expression for small and large r_12 and compute the determinant numerically for arbitrary r_12 and v.Comment: 17 pages, published version, references adde

Interaction Energy of `t Hooft-Polyakov Monopoles

The dependence of the energies of axially symmetric monopoles of magnetic charges 2 and 3, on the Higgs self-interaction coupling constant, is studied numerically. Comparing the energy per unit topological charge of the charge-2 monopole with the energy of the spherically symmetric charge-1 monopole, we confirm that there is only a repulsive phase in the interaction energy between like monopolesComment: 6 pages, including 1 postscript figure, LaTex2e forma

N=(0,2) Deformation of the N=(2,2) Wess-Zumino Model in Two Dimensions

We construct a simple N=(0,2) deformation of the two-dimensional Wess-Zumino model. In addition to superpotential, it includes a "twisted" superpotential. Supersymmetry may or may not be spontaneously broken at the classical level. In the latter case an extra right-handed fermion field \zeta_R involved in the N=(0,2) deformation plays the role of Goldstino.Comment: 6 pages; v2: 3 references added; final version accepted for publication in PR

Nonminimal Maxwell-Chern-Simons-O(3)-sigma vortices: asymmetric potential case

In this work we study a nonlinear gauged O(3)-sigma model with both minimal and nonminimal coupling in the covariant derivative. Using an asymmetric scalar potential, the model is found to exhibit both topological and non-topological soliton solutions in the Bogomol'nyi limit.Comment: 4 pages, 4 figures. Some typos corrected, two references changed. To appear in Physical Review

Effect of quantum fluctuations on topological excitations and central charge in supersymmetric theories

The effect of quantum fluctuations on Bogomol'nyi-Prasad-Sommerfield (BPS)-saturated topological excitations in supersymmetric theories is studied. Focus is placed on a sequence of topological excitations that derive from the same classical soliton or vortex in lower dimensions and it is shown that their quantum characteristics, such as the spectrum and profile, differ critically with the dimension of spacetime. In all the examples examined the supercharge algebra retains its classical form although short-wavelength fluctuations may modify the operator structure of the central charge, yielding an anomaly. The central charge, on taking the expectation value, is further affected by long-wavelength fluctuations, and this makes the BPS-excitation spectra only approximately calculable in some low-dimensional theories. In four dimensions, in contrast, holomorphy plays a special role in stabilizing the BPS-excitation spectra against quantum corrections. The basic tool in our study is the superfield supercurrent, from which the supercharge algebra with a central extension is extracted in a supersymmetric setting. A general method is developed to determine the associated superconformal anomaly by considering dilatation directly in superspace.Comment: 10 pages, Revtex, to appear in PR

Calorons in SU(3) lattice gauge theory

We examine the semiclassical content of SU(3) Yang Mills theory on the lattice at finite temperature. Employing the cooling method, a set of classical fields is generated from a Monte Carlo ensemble. Various operators are used to inspect this set with respect to topological properties. We find pseudoparticle fields, so-called caloron solutions, possessing the remarkable features of (superpositions of) Kraan-van Baal solutions, i.e. extensions of Harrington-Shepard calorons to generic values of the holonomy.Comment: 14 pages, 16 figure

Cosmic string Y-junctions: a comparison between field theoretic and Nambu-Goto dynamics

We explore the formation of cosmic string Y-junctions when strings of two different types collide, which has recently become important since string theory can yield cosmic strings of distinct types. Using a model containing two types of local U(1) string and stable composites, we simulate the collision of two straight strings and investigate whether the dynamics matches that previously obtained using the Nambu-Goto action, which is not strictly valid close to the junction. We find that the Nambu-Goto action performs only moderately well at predicting when the collision results in the formation of a pair of Y-junctions (with a composite string connecting them). However, we find that when they do form, the late time dynamics matches those of the Nambu-Goto approximation very closely. We also see little radiative emission from the Y-junction system, which suggests that radiative decay due to bridge formation does not appear to be a means via which a cosmological network of such string would rapidly lose energy.Comment: 17 pages, 17 figures; typo correctio