Organized by:
Scott Collier (Syracuse University)
Gerald Dunne (University of Connecticut)
Michael Gutperle (UCLA)
Nikita Nekrasov (SCGP)
Maxim Zabzine (Uppsala University)
One deforms the contour of path integration into the complex domain, so as to achieve
better approximation, and more ambitiously, potentially exact results. The saddle points of the analytically continued action functional dominate the integral. They also determine the possible choices of the contours. One option for such a contour is the Lefschetz thimble, which depends on additional data, such as the choice of hermitian metric on the complexified space of fields. The path integral computing correlation functions or S-matrix elements splits as a sum of periods over several, possibly infinitely many, thimbles, each corresponding to a critical point of the action in the space of complexified fields. Unlike the dilute instanton gas approximation, which only works in simple quantum mechanical models, the honest complex saddle points should give a reliable picture of non-perturbative quantum field theory, and perhaps even gravity.
One deforms the contour of path integration into the complex domain, so as to achieve
better approximation, and more ambitiously, potentially exact results. The saddle points of the analytically continued action functional dominate the integral. They also determine the possible choices of the contours. One option for such a contour is the Lefschetz thimble, which depends on additional data, such as the choice of hermitian metric on the complexified space of fields. The path integral computing correlation functions or S-matrix elements splits as a sum of periods over several, possibly infinitely many, thimbles, each corresponding to a critical point of the action in the space of complexified fields. Unlike the dilute instanton gas approximation, which only works in simple quantum mechanical models, the honest complex saddle points should give a reliable picture of non-perturbative quantum field theory, and perhaps even gravity. the study of complex saddle points and perturbation theory around them, the multiplicity of the associated Lefschetz thimbles contribution to the physical amplitude is as timely and crucial as it ever was.