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

TL;DR

This paper explores an extended $ abla$2 supersymmetry with central charge, developing its superspace formulation in classical mechanics and field theory, and analyzing topological solutions in a two-dimensional model.

Contribution

It introduces a novel superspace formulation for $ abla$2 supersymmetry with central charge in both mechanics and field theory contexts.

Findings

Deformed supersymmetric derivatives in classical mechanics.

Implementation of superalgebra in two-dimensional field theory.

Identification of non-trivial fermionic solutions in a topological matter model.

Abstract

In this work, we analyze an extended $\mathcal{N}=2$ 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 non-linear 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 non-trivial fermionic solution.