Tying up instantons with anti-instantons

Nikita Nekrasov

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

9 Citations (Scopus)

Abstract

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.
Pages351-388
Number of pages38
ISBN (Electronic)9789813233867
ISBN (Print)9789813233768
DOIs
Publication statusPublished - 1 Jan 2018
Externally publishedYes

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