Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the Stability of the GPS Magnetic Monopole Solution
55
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The question of the stability of the four dimensional Gross-Perry-Sorkin Kaluza-Klein magnetic monopole solution is investigated within the framework of a N=2, D=5 supergravity theory. We show that this solution does not support a spin structure of the Killing type and is therefore, contrary to previous expectations, not necessarily stable.
rate research
Read More
As shown by Taubes, in the Bogomolnyi-Prasad-Sommerfield limit the SU(2) Yang-Mills-Higgs model possesses smooth finite energy solutions, which do not satisfy the first order Bogomolnyi equations. We construct numerically such a non-Bogomolnyi solution, corresponding to a monopole-antimonopole pair, and extend the construction to finite Higgs potential.
We present simulations of one magnetic monopole interacting with multiple magnetic singularities. Three-dimensional plots of the energy density are constructed from explicit solutions to the Bogomolny equation obtained by Blair, Cherkis, and Durcan. Animations follow trajectories derived from collective coordinate mechanics on the multi-centered Taub--NUT monopole moduli space. We supplement our numerical results with a complete analytic treatment of the single-defect case.
At classical level, dynamical derivation of the properties and conservation laws for topologically non-trivial systems from Noether theorem versus the derivation of the systems properties on topological grounds are considered as distinct. We do celebrate any agreements in results derived from these two distinct approaches: i.e. the dynamical versus the topological approach. Here we consider the Corrigan-Olive-Fairlie-Nuyts solution based on which we study the stability of the t Hooft- Polyakov outer field, known as its Higgs vacuum, and derive its stability, dynamically, from the equations of motion rather than from the familiar topological approach. Then we use our derived result of the preservation of the Higgs vacuum asymptotically to derive the stability of the t Hooft-Polyakov monopole, even if inner core is perturbed, where we base that on observing that the magnetic charge must be conserved if the Higgs vacuum is preserved asymptotically. We also, alternatively, note stability of t Hooft-Polyakov monopole and the conservation of its magnetic charge by again using the result of the Higgs vacuum asymptotic preservation to use Eq.(5) to show that no non-Abelian radiation allowed out of the core as long as the Higgs vacuum is preserved and restored, by the equations of motion, if perturbed. We start by deriving the asymptotic equations of motion that are valid for the monopoles field outside its core; next we derive certain constraints from the asymptotic equations of motion of the Corrigan-Olive-Fairlie-Nuyts solution to the t Hooft-Polyakov monopole using the Lagrangian formalism of singular theories, in particular that of Gitman and Tyutin. The derived constraints will show clearly the stability of the monopoles Higgs vacuum its restoration by the equations of motion of the Higgs vacuum, if disturbed.
The Witten effect tells that a unit magnetic monopole can bind a half elementary charge in an axion media. We present an exact solution of a magnetic monopole in a topological insulator that was proposed to be an axion media recently. It is found that a magnetic monopole can induce one zero energy state bound to it and one surface state of zero energy. The two states are quite robust, but the degeneracy can be removed by external fields. For a finite size system, the interference of two states may lift the degeneracy, and the resulting states have one half near the origin and another half around the surface, which realizes the Witten effect. However, the energy difference decays exponentially with the size of the system. The exact solution does not fully support the realization of the Witten effect in a topological insulator.
We propose a new definition for the abelian magnetic charge density of a non-abelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose expansion in powers of 1/r agrees with that of the conventional asymptotic magnetic field to all orders. We also show that the asymptotic field can be easily calculated from the spectral curve. Explicit examples are given for known monopole solutions.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
