Localized Fermions on Superconducting Domain Walls and Extended Supersymmetry with Non-trivial Topological Charges

In this letter we demonstrate that the fermionic zero modes on a superconducting domain wall can be associated to an one dimensional N=6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=6$$\end{document} supersymmetry that contains non-trivial topological charges. In addition, the system also possesses three distinct N=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=4$$\end{document} supersymmetries with non-trivial topological charges and we also study some duality transformations of the supersymmetric algebras.