Isospin particle on $S^{2}$ with arbitrary number of supersymmetries

Details Isospin particle on $S^{2}$ with arbitrary number of supersymmetries Isospin particle on $S^{2}$ with arbitrary number of supersymmetries

2006-06-21

arxiv.org/abs/hep-th/0606202v2

Mod.Phys.Lett.A22:1481-1492,2007

Physics

High Energy Physics

High Energy Physics - Theory

6 pages

Scientific paper

10.1142/S0217732307023857

We study the supersymmetric quantum mechanics of an isospin particle in the background of spherically symmetric Yang-Mills gauge field. We show that on $S^{2}$ the number of supersymmetries can be made arbitrarily large for a specific choice of the spherically symmetric SU(2) gauge field. However, the symmetry algebra containing the supercharges becomes nonlinear if the number of fermions is greater than two. We present the exact energy spectra and eigenfunctions, which can be written as the product of monopole harmonics and a certain isospin state. We also find that the supersymmetry is spontaneously broken if the number of supersymmetries is even.

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