Valley Views: Instantons, Large Order Behaviors, and Supersymmetry

Details Valley Views: Instantons, Large Order Behaviors, and Supersymmetry Valley Views: Instantons, Large Order Behaviors, and Supersymmetry

1998-08-06

arxiv.org/abs/hep-th/9808034v1

Nucl.Phys. B553 (1999) 644-710

Physics

High Energy Physics

High Energy Physics - Theory

78 pages, Latex, 22 eps figures

Scientific paper

10.1016/S0550-3213(99)00263-1

The elucidation of the properties of the instantons in the topologically trivial sector has been a long-standing puzzle. Here we claim that the properties can be summarized in terms of the geometrical structure in the configuration space, the valley. The evidence for this claim is presented in various ways. The conventional perturbation theory and the non-perturbative calculation are unified, and the ambiguity of the Borel transform of the perturbation series is removed. A `proof' of Bogomolny's ``trick'' is presented, which enables us to go beyond the dilute-gas approximation. The prediction of the large order behavior of the perturbation theory is confirmed by explicit calculations, in some cases to the 478-th order. A new type of supersymmetry is found as a by-product, and our result is shown to be consistent with the non-renormalization theorem. The prediction of the energy levels is confirmed with numerical solutions of the Schr\"{o}dinger equation.

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