# Extended supersymmetry with central charges in Dirac action with curved extra dimensions

## TL;DR

This paper reveals a hidden extended supersymmetry structure in the mass spectrum of higher-dimensional Dirac fields with curved extra dimensions, linking symmetries in extra dimensions to supersymmetric quantum mechanics and explaining spectral degeneracies.

## Contribution

It introduces a novel realization of extended quantum-mechanical supersymmetry with central charges in higher-dimensional Dirac actions with curved extra dimensions, connecting it to geometric symmetries and BPS states.

## Key findings

- Extended supersymmetry explains degeneracies in the 4D mass spectrum.
- Symmetries in extra dimensions lead to hidden supersymmetry structures.
- The model with $S^2$ extra dimension and magnetic monopole confirms the theory.

## Abstract

We discuss a new realization of $\mathcal{N}$-extended quantum-mechanical supersymmetry (QM SUSY) with central charges hidden in the four-dimensional (4D) mass spectrum of higher dimensional Dirac action with curved extra dimensions. We show that this $\mathcal{N}$-extended QM SUSY results from symmetries in extra dimensions, and the supermultiplets in this supersymmetry algebra correspond to the Bogomol'nyi--Prasad--Sommerfield states. Furthermore, we examine the model of the $S^2$ extra dimension with a magnetic monopole background and confirm that the $\mathcal{N}$-extended QM SUSY explains the degeneracy of the 4D mass spectrum.