Extended supersymmetry in Dirac action with extra dimensions

Abstract

We investigate a new realization of extended quantum-mechanical supersymmetry. We first show that an $\mathcal{N}=2$ quantum-mechanical supersymmetry is hidden in the four-dimensional (4D) spectrum of the Kaluza-Klein decomposition for the higher dimensional Dirac field, that is, Kaluza-Klein mode functions of 4D right-handed spinors and 4D left-handed ones form $\mathcal{N}=2$ supermultiplets. In addition to $\mathcal{N}=2$ supersymmetry, we discover that an $\mathcal{N}$-extended supersymmetry ($\mathcal{N}=d+2(d+1)$ for $d=$ even (odd) extra dimensions) is further hidden in the 4D spectrum. The extended symmetry can explain additional degeneracy of the spectrum. Furthermore, we show that a superpotential can be introduced into the $\mathcal{N}$-extended supercharges and clarify the condition to preserve the supersymmetry. The partial breaking of the supersymmetry is also demonstrated.

arXiv comment11 pages, 3 figures

References in corpus (20)

• Supersymmetry and Quantum Mechanics
• Black Holes and Superconformal Mechanics
• Infinitely many shape invariant potentials and new orthogonal polynomials
• Dirac oscillator with nonzero minimal uncertainty in position
• Supersymmetric SYK model and random matrix theory
• Adinkras: A Graphical Technology for Supersymmetric Representation Theory
• On the Classification of N-extended Supersymmetric Quantum Mechanical Systems
• Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry
• Supersymmetric Quantum Mechanics
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Extended Supersymmetric Quantum Mechanics
• Energy-momentum/Cotton tensor duality for AdS4 black holes
• Supersymmetry in gauge theories with extra dimensions
• Supersymmetry in 5d Gravity
• Gauge-Fixing and Residual Symmetries in Gauge/Gravity Theories with Extra Dimensions
• Supersymmetry and discrete transformations on S^1 with point singularities
• Extended supersymmetry and its reduction on a circle with point singularities
• 6d Dirac fermion on a rectangle; scrutinizing boundary conditions, mode functions and spectrum
• Emergent Supersymmetry in Warped Backgrounds
• Extended Supersymmetric Quantum Mechanics of Fierz and Schur Type