Towards Lefschetz thimbles in field theory

Abstract: I will review the quantization procedure viewed from a higher dimensional perspective: old-fashioned path integrals, Kontsevich Poisson sigma model, cc branes of Kapustin-Orlov, and, finally, four dimensional Omega-deformed N=2 gauge theories. By rephrasing the computation of quantum model partition function in four dimensional language we arrive at the motivation to search for critical points of analytically continued (complexified) action functional. I will then report on the recent progress (in a joint work with I.Krichever) in this problem in the case of two dimensional sigma models, notably with the target spaces being the spheres and complex projective spaces.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar