Narrow Results

We study the supersymmetric quantum mechanics of an isospin particle in the background of spherically symmetric Yang–Mills gauge field. We show that on S² 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.

Motivated by the Nahm’s construction, in this paper, we present a systematic construction of Schrödinger Hamiltonians for a spin-1/2 particle where the Berry connection in the ground-state sector becomes the Bogomolny–Prasad–Sommerfield (BPS) monopole of SU(2) Yang–Mills–Higgs theory. Our construction enjoys a single arbitrary monotonic function, thereby creating infinitely many quantum-mechanical models that simulate the BPS monopole in the space of model parameters.