Anomalous SUSY quantum mechanics, heterotic models and scattering states

We analyze the symmetry breaking associated to anomalous realization of supersymmetry in the context of Supersymmetric Quantum Mechanics (SUSY QM). We show how the supercharge itself might become an anomalous operator in the process of quantization. We study a solvable potential in the Poschl-Teller class containing both bound states and continuous spectrum. We find a situation reminiscent of the heterotic string: one of the two SUSY partners lives in the whole real axis while the other restricts itself to the half-line. Peculiarities of the model include negative energies, incomplete pairing of states and anomalous behavior for the phase shifts in scattering.