Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary

Abstract

We extend duality between the quantum integrable Gaudin models with boundary and the classical Calogero–Moser systems associated with root systems of classical Lie algebras B N , C N , D N to the case of supersymmetric gl(m|n) Gaudin models with m + n = 2. Namely, we show that the spectra of quantum Hamiltonians for all such magnets being identified with the classical particles velocities provide the zero level of the classical action variables.