Instantons and Borel resummability for the perturbed supersymmetric anharmonic oscillator

In this paper we give an analytical derivation of the large-order behavior of the perturbation series for both the ground state and the excited states of the supersymmetric anharmonic oscillator and of the anharmonic oscillator obtained from the supersymmetric case by varying the strength of the fermion coupling. The results which are obtained with the help of instanton calculus coincide with those obtained numerically in previous work. The large-order perturbation series of the ground state vanishes in the supersymmetric case, whereas away from the supersymmetric point the perturbation series diverges factorially. The perturbation series of the excited states diverges factorially both at the supersymmetric point and away from this point.