Tying up instantons with anti-instantons

Nikita Nekrasov

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

9 Citations (Scopus)


In quantizing classical mechanical systems, one often sums over the classical trajectories as in localization formulas, but also takes into account the contributions of the “instanton gas”: a set of approximate solutions of the equations of motion. This paper attempts to alleviate some of the frustrations of this 40+ year-old approach by finding the honest solutions of equations of motion of the complexified classical mechanical system. These ideas originated in the Bethe/gauge correspondence. The examples include algebraic integrable systems, from the abstract Hitchin systems to the well-studied anharmonic oscillator. We also speculate on the applications to the black hole radiation. We elucidate the relation between Lefschetz thimbles and the O-deformed B-model. We propose the notion of the topological renormalization group.

Original languageEnglish
Title of host publicationLudwig Faddeev Memorial Volume
Subtitle of host publicationA Life in Mathematical Physics
PublisherWorld Scientific Publishing Co.
Number of pages38
ISBN (Electronic)9789813233867
ISBN (Print)9789813233768
Publication statusPublished - 1 Jan 2018
Externally publishedYes


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