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

Inori Ueba

doi:10.1103/physrevd.100.105001

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.

Highlights

Since not so many models which realize arbitrary large N -extended quantum-mechanical supersymmetry (QM SUSY) with central charges are known, it is worth investigating a new realization of N -extended one
In the previous papers [44,45], we have revealed that this N 1⁄4 2 QM SUSY can be extended to the N -extended QM SUSY from the reflection symmetries in the flat extra dimensions
In this paper, we discuss a new realization of the N -extended QM SUSY with central charges which are obtained from symmetries in the higher dimensional Dirac action with curved extra dimensions

Summary

INTRODUCTION

Quantum-mechanical supersymmetry (QM SUSY) has attracted much attention and has been applied to the various research areas, e.g., exactly solvable quantum mechanics [1,2,3,4], Berry phase [5,6,7], black holes and AdS/ CFT [8,9,10,11,12], Sachdev–Ye–Kitaev model [13,14,15,16,17], extra dimensional models [18,19,20,21,22,23] and so on. We have found that the central charges appear as the result of the reflection symmetries, and the supermultiplets of this extended QM SUSY corresponds to the BPS states These supercharges can explain the degeneracy of the 4D mass spectrum. In this paper, we discuss a new realization of the N -extended QM SUSY with central charges which are obtained from symmetries in the higher dimensional Dirac action with curved extra dimensions. Dirac action and the doubly degenerate states ðf and ð0; gðαnÞðyÞÞT are mutually related by the supercharge Q, except for zero energy states

N -EXTENDED QM SUSY WITH CENTRAL CHARGES

Representation of SUSY algebra

EXAMPLE

N -extended QM SUSY in S2-extra dimension with magnetic monopole

SUMMARY AND DISCUSSION