Abelian and non-Abelian Hopfions in all odd dimensions

Tangled Magnetic Fields in Astro- and Plasma Physics; Quantised Flux in Tightly Knotted and Linked Systems

Radu, Eugen^1 ; Tchrakian, Tigran^2,3

Institut für Physik, Universität Oldenburg, Postfach 2503, Oldenburg

D-26111, Germany^1

School of Theoretical Physics-DIAS, 10 Burlington Road, Dubline 4, Ireland^2

Department of Computer Science, Maynooth University, Ireland^3

关键词: Composite connections;    Grassmannian;    Higher dimensions;    Sigma model;    Topological charges;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/544/1/012024/pdf
DOI  :  10.1088/1742-6596/544/1/012024

来源: IOP

【 摘 要 】

We extend the definition of the topological charge pertaining to the CP1(i.e. O(3)) Skyrme-Fadde'ev Hopfion on3to candidates for topological charges of Pnsigma models on2n+1for all n. For this, the Abelian composite connections of the Pnsigma models are employed. In higher dimensions (n ≥ 1) it turns out that such charges, described by the nonAbelian composite connections of suitable Grassmannian sigma models, can also be constructed. A concrete discussion of the non-Abelian case for n 2 is presented.