Supersymmetry and exceptional points

Abstract

A conceptual bridge is provided between SUSY and the three-Hilbert-space upgrade of quantum theory a.k.a. ${\cal PT}-$symmetric or quasi-Hermitian. In particular, a natural theoretical link is found between SUSY and the presence of Kato's exceptional points (EPs), both being related to the phenomenon of degeneracy of energy levels. Regularized spiked harmonic oscillator is recalled for illustration.