Superconducting cosmic strings and one dimensional extended supersymmetric algebras

In this article we study in detail the supersymmetric structures that underlie the system of fermionic zero modes around a superconducting cosmic string. Particularly, we extend the analysis existing in the literature on the one dimensional N=2N=2 supersymmetry and we find multiple N=2N=2, d=1d=1 supersymmetries. In addition, compact perturbations of the Witten index of the system are performed and we find to which physical situations these perturbations correspond. More importantly, we demonstrate that there exists a much more rich supersymmetric structure underlying the system of fermions with NfNf flavors and these are NN-extended supersymmetric structures with non-trivial topological charges, with “NN” depending on the fermion flavors.