# Extended supersymmetry with central charges in higher dimensional Dirac action

## TL;DR

This paper uncovers hidden extended quantum-mechanical supersymmetry with central charges in the 4D mass spectrum of higher-dimensional Dirac actions, revealing new algebraic structures and supersymmetric states.

## Contribution

It demonstrates the existence of hidden extended supersymmetry with central charges in the spectra of higher-dimensional Dirac models, providing explicit algebraic structures and spectrum analysis.

## Key findings

- Hidden supersymmetry algebras with central charges are found in 4D spectra.
- Supersymmetric states correspond to 1/2-BPS states with short representations.
- Explicit spectrum analysis for models with hyperrectangle and torus extra dimensions.

## Abstract

A new realization of extended quantum-mechanical supersymmetry (QM SUSY) with central extension is investigated. We first show that two different sets of $d+2$ ($d+1$) supercharges for $d=$ even (odd), each of which satisfies an $\mathcal{N}=d+2$ ($d+1$) extended QM SUSY algebra without central extension, are hidden in the four-dimensional (4D) mass spectrum of the $(4+d)$-dimensional Dirac action. We then find that the whole set of the supercharges forms an $\mathcal{N}=2d+4$ ($2d+2$) extended QM SUSY algebra with central charges for $d=$ even (odd). The representation of the supersymmetry algebra is shown to be $1/2$-Bogomol'nyi--Prasad--Sommerfield states that correspond to a short representation for the supersymmetry algebra with central extension. We explicitly examine the 4D mass spectrum of the models with the hyperrectangle and the torus extra dimensions, and discuss their supersymmetric structures.