title: Complexified Path Integrals, Exact Saddles, and Supersymmetry.
abstract: In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semiclassical 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 semiclassical expansion is in conflict with basic properties such as the positive semidefiniteness of the spectrum, as well as constraints of supersymmetry. Generic saddles are not only complex, but also possibly multivalued and even singular. This is in contrast to instanton solutions, which are real, smooth, and single valued. The multivaluedness of the action can be interpreted as a hidden topological angle, quantized in units of π in supersymmetric theories. The general ideas also apply to nonsupersymmetric theories.
authors.affiliation: Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA.|Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Alireza
authors.initials: A
authors.lastname: Behtash
authors.affiliation: Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA.
authors.forename: Gerald V
authors.initials: GV
authors.lastname: Dunne
authors.affiliation: Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA.
authors.forename: Thomas
authors.initials: T
authors.lastname: Schäfer
authors.affiliation: Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA.
authors.forename: Tin
authors.initials: T
authors.lastname: Sulejmanpasic
authors.affiliation: Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA.|Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Mithat
authors.initials: M
authors.lastname: Ünsal