Bootstrapping instantons with antiinstantons

by Nikita Nekrasov (IHES)

Wednesday 21 Feb 2018, 14:00 → 15:30 Europe/Zurich

4/3-006 - TH Conference Room (CERN)

In quantizing classical mechanical systems to get  (the corrections, non-perturbative in h-bar) the eigenvalues of the Hamiltonian one often sums over the classical trajectories as in localization formulas, but also takes into account the contributions of the "instanton -- anti-instanton gas": an ill-defined set of approximate solutions of equations of motion. In the lecture we attempt to alleviate some of the frustrations of this 40+ yrs old approach by making use of honest solutions of equations of motion of the complexified classical mechanical system. The examples will include algebraic integrable systems, from the abstract Hitchin systems to the well-studied anharmonic oscillator. These ideas originate in the Bethe/gauge correspondence.