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An inextricable link: semi-classics and complex saddles

I will discuss the use of semi-classics and instanton calculus and argue that, contrary to common wisdom, complex solutions of the equations of motion are a necessary ingredient of a semi-classical expansion. In particular, I will show that without the complex solutions semi-classics is unable to explain some elementary physics of supersymmetry. The use of complex saddles has a natural interpretation in the Picard-Lefschetz theory.