Vortex dynamics in classical non-Abelian spin models

We discuss the Abelian vortex dynamics in the Abelian projection approach to non-Abelian spin models. We show numerically that in the three-dimensional SU(2) spin model in the maximal Abelian projection the Abelian off-diagonal vortices, unlike the diagonal vortices, are not responsible for the phase transition. A generalization of the Abelian projection approach to SU(N) spin models is briefly discussed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 526–530 (25 April 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Dyon condensation and the Aharonov-Bohm effect

We derive the string representation of the Abelian Higgs theory in which dyons are condensed. It happens that in such a representation the topological interaction exists in the expectation value of the Wilson loop. Due to this interaction the dynamics of the string spanned on the Wilson loop is nontrivial. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 6, 367–371 (25 March 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Localized gravity on topological Abelian Higgs strings

In this work there are proposed several new 6D brane worlds based on exact topological solutions to the vortex equations for the Abelian Higgs model, with suitable boundary conditions and symmetry breaking potentials similar to the mexican hat. Just as happens for RS domain wall brane worlds, it is shown that the massless mode of linearized gravity is localized in the neighborhood of the string–vortex solution while there are not massive bounded states. The correction to the newtonian limit of the effective 4D gravity is calculated.     

On Vortex Dynamics in the Self-Dual Chern–Simons–Higgs System

The dynamics of n vortices in the self-dual Chern–Simons–Higgs system defined on the infinite plane is investigated. In adiabatic approximation, the vortex dynamics is determined by considering a rigid motion of a vortex configuration and a motion around a fixed center of mass. A motion of two vortices is studied in detail.     

Complete control of gauge parameter dependence in the Abelian Higgs model

We examine the dependence on all gauge parameters in the example of the Abelian Higgs model by applying a general algebraic method which roots in an extension of the usual Slavnov-Taylor identity. This method automatically yields all information about the gauge parameter dependence of Green functions and therefore especially allows to control the range of “good” normalization conditions. In this context we show that the physical on-shell normalization conditions are in complete agreement with the restrictions dictated by the enlarged Slavnov-Taylor identity and that the coupling can be fixed in an easily handleable way on the Ward identity of local gauge invariance. As an application of the general method we also study the Callan-Symanzik equation and the renormalization group equation of the Abelian Higgs model. Received: 18 July 1997 / Revised version: 20 October 1997 / Published online: 23 February 1998     

Multivortex Solutions in (2+1)-Dimensional Abelian Higgs Model with a Chern-Simons Term

The multivortex solutions of (2+l)-dimensional Abelian Higgs model with a Chern-Simons term are stlrrlied. The Bogomol'nyi-type equations and corresponding Weinberg's index theorem have been derived for a sixth-order Higgs potential. The magnetic field is different from that of the Abelian Chern-Simons Higgs model which has no Maxwell term, and has a maximum at the center of the vortex.     

Vector boson decays of the Higgs boson

We derive the width of the Higgs boson into vector bosons. General formulas are derived both for the on–shell decay as well for the off–shell decays, and , where . For the off-shell decays the width of the decaying vector boson is properly included. The formulas are valid both for the Standard Model as well as for arbitrary extensions. As an example we study in detail the gauge-invariant effective Lagrangian models where we can have sizable enhancements over the Standard Model that could be observed at LEP. Received: 31 July 1998 / Revised version: 23 September 1998 / Published online: 6 November 1998     

Charged Vortices in an Abelian Higgs Model with Chern-Simons Term at Finite Temperature

Charged vortex solutions are found iri a (2+1)-dimensional Abelian Higgs model with Chern- Simons term at finite temperature. It is shown that there exists a finite critical temperature at which vortices disappear and it implies that the system changes fiom superconducting state to normal state at this critical temperature.     

Fermionic string from Abelian Higgs model with monopoles and Θ-term

The four-dimensional Abelian Higgs model with monopoles and Θ-term is considered in the limit of large mass of the Higgs boson. We show that for Θ=2π the theory is equivalent, at large distances, to summation over all possible world-sheets of fermionic strings with Dirichlet-type boundary conditions on the string coordinates. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 76–80 (25 July 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Non-Topological Solutions of the Relativistic SU(3) Chern–Simons Higgs Model

In this paper, we obtain non-topological solutions of the self-dual equations arising in the relativistic SU(3) Chern–Simons Higgs model. Received: 11 July 1998 / Accepted: 1 November 1998     

对偶超导模型n=90—110的近似解析解

研究了对偶超导模型的大n涡旋。 基于变分原理得出了Abelian Higgs模型在n=90—110的近似涡旋解析解, 并计算了涡旋张力对n的依赖性。 发现, 每根涡旋的张力大致随n线性增长。 期望该解对理解Abelian Higgs模型中的大量子数涡旋的墙行为具有一定价值。 The large n vortices in the dual superconductor model was investigated. An approximate analytical solution was obtained for n fold quantized vortices with n=90—110 by variationally solving the AbelianHiggs model, and the vortex tension was calculated as a function of n. It was found that the vortex tension rises linearly as n grows. It is hoped that our solution shines light on the understanding of the wall behavior of the large n vortices in Abelian Higgs model.     

The Stability of Magnetic VorticesRID="*"ID="*"Research on this paper was supported by NSERC under grant N7901

We study the linearized stability of n-vortex (n∈ℤ) solutions of the magnetic Ginzburg–Landau (or Abelian Higgs) equations. We prove that the fundamental vortices (n = ± 1) are stable for all values of the coupling constant, λ, and we prove that the higher-degree vortices (|n|≥ 2) are stable for λ < 1, and unstable for λ > 1. This resolves a long-standing conjecture (see, eg, [JT]). Received: 16 November 1998 / Accepted: 3 January 2000 RID="*" ID="*"Research on this paper was supported by NSERC under grant N7901 RID="**" ID="**"Present address: Courant Institute, 251 Mercer St., New York, NY 10012, USA.&para;E-mail: gustaf&commat;cims.nyu.edu     

BPS solutions to a generalized Maxwell–Higgs model

We look for topological BPS solutions of an Abelian Maxwell–Higgs theory endowed by non-standard kinetic terms to both gauge and scalar fields. Here, the non-usual dynamics are controlled by two positive functions, G(|ϕ|) and w(|ϕ|), which are related to the self-dual scalar potential V(|ϕ|) of the model by a fundamental constraint. The numerical results we found present interesting new features, and contribute to the development of the recent issue concerning the study of generalized models and their applications.     

Chern–Simons particles with nonstandard gravitational interaction

The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity is extended to include Abelian or non-Abelian charges coupled to Chern–Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern–Simons particles coupled, in a reparameterization invariant way, to a translational Chern–Simons action. The quantum 2-body problem is described by a nonstandard Schr?dinger equation with a noninteger angular momentum depending on energy as well as particle charges. Some numerical results describing the modification of the energy levels by these charges in the confined regime are presented. The modification involves a shift as well as splitting of the levels. Received: 16 March 2001 / Published online: 13 June 2001     

Two Higgs Doublet Model and model independent interpretation of neutral Higgs boson searches

Searches for the neutral Higgs bosons and are used to obtain limits on the Type II Two Higgs Doublet Model (2HDM(II)) with no CP–violation in the Higgs sector and no additional particles besides the five Higgs bosons. The analysis combines approximately 170 pb of data collected with the OPAL detector at GeV with previous runs at and GeV. The searches are sensitive to the and decay modes of the Higgs bosons. For the first time, the 2HDM(II) parameter space is explored in a detailed scan, and new flavour independent analyses are applied to examine regions in which the neutral Higgs bosons decay predominantly into light quarks or gluons. Model–independent limits are also given. Received: 11 July 2000 / Published online: 21 December 2000     

Are vortex numbers preserved?

We study noncommutative vortex solutions that minimize the action functional of the Abelian Higgs model in 2-dimensional noncommutative Euclidean space. We first consider vortex solutions which are deformed from solutions defined on commutative Euclidean space to the noncommutative one. We construct solutions whose vortex numbers are unchanged under the noncommutative deformation. Another class of noncommutative vortex solutions via a Fock space representation is also studied.     

Three-dimensional Abelian Higgs model: Confinement and the Aharonov-Bohm effect

The Aharonov-Bohm effect in a lattice noncompact Abelian Higgs model in 2+1 space-time is studied. It is shown numerically and analytically that this effect results in a long-range logarithmic interaction of charged particles. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 7, 492–495 (10 April 1996)     

Ordering of interacting subsystems. Molecular dynamics

The molecular dynamics method is used to examine the ordering of interacting subsystems in a two-component, two-dimensional Coulomb gas, consisting of equal amounts of positively and negatively charged particles, which simulates the behavior of a system of interacting vortices. In particular, it is found that when the system temperature is lowered from the Kosterlitz-Thouless transition point, additional ordering of the vortex chains may take place. It is noted that this process may stimulate the development of vortex chains observed in real superfluid, magnetic, and superconducting systems. Possible applications of the molecular dynamics method to phase separation and the ordering of adiabatically slowly moving subsystems in the collective field of a fast subsystem are considered. Fiz. Tverd. Tela (St. Petersburg) 40, 1701–1704 (September 1998)     

Wave functions and spectrum in hot electroweak matter for large Higgs masses

We present results for the wave functions and the screening mass spectrum for quantum numbers , and in the three-dimensional SU(2)–Higgs model near to the phase transition line below the endpoint and in the crossover region. Varying the 3D gauge couplings we study the behaviour along a line of constant physics towards the continuum limit in both phases. In the crossover region the changing spectrum of screening states versus temperature is examined showing the aftermath of the phase transition at lower Higgs mass. Different to smearing concepts we used large sets of operators with various extensions allowing to identify wave functions in position space. Received: 4 August 1998 / Published online: 2 November 1998     

Self Duality Equations for Ginzburg–Landau¶and Seiberg–Witten Type Functionals¶with 6th Order Potentials

The abelian Chern–Simons–Higgs model of Hong-Kim-Pac and Jackiw–Weinberg leads to a Ginzburg–Landau type functional with a 6^th order potential on a compact Riemann surface. We derive the existence of two solutions with different asymptotic behavior as the coupling parameter tends to 0, for any number of prescribed vortices. We also introduce a Seiberg–Witten type functional with a 6^th order potential and again show the existence of two asymptotically different solutions on a compact K?hler surface. The analysis is based on maximum principle arguments and applies to a general class of scalar equations. Received: 13 October 1998 / Accepted: 21 October 2000