# $\mathcal{N}=2$ Supersymmetry with Central Charge: A Twofold Implementation

Ospedal, L. P. R.  (Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr. Xavier Sigaud 150, Urca, Rio de Janeiro, CEP 22290-180, Brazil) ; Terin, R. C. (Universidade do Estado do Rio de Janeiro (UERJ), Instituto de Física, Departamento de Física Teórica, Rua São Francisco Xavier 524, Maracanã, Rio de Janeiro, CEP 20550-013, Brazil) (Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, 75005 Paris, France)

23 January 2019

Abstract: In this work, we analyze an extended $\mathcal{N}=\mathrm{2}$ supersymmetry with central charge and develop its superspace formulation under two distinct viewpoints. Initially, in the context of classical mechanics, we discuss the introduction of deformed supersymmetric derivatives and their consequence on the deformation of one-dimensional nonlinear sigma model. After that, considering a field-theoretical framework, we present an implementation of this superalgebra in two dimensions, such that one of the coordinates is related to the central charge. As an application, in this two-dimensional scenario, we consider topological (bosonic) configurations of a special self-coupled matter model and present a nontrivial fermionic solution.

Published in: Advances in High Energy Physics 2019 (2019) 8604386