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2015

Complexified path integrals, exact saddles and supersymmetry

Behtash, Alireza, Dunne, Gerald V., Schaefer, Thomas et al.

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In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real.

We find new exact complex saddles, and show that without their contribution the semi-classical expansion is in conflict with basic properties such as positive-semidefiniteness of the spectrum, and constraints of supersymmetry.
Generic saddles are not only complex, but also possibly multi-valued, and even singular.
This is in contrast to instanton solutions, which are real, smooth, and single-valued.

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