2018/02/12 by Nikita Nekrasov, Nekrasov, Nikita · 2 citations
Computer Science · Physics and Astronomy · #Algorithms and Data Compression #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Metaheuristic Optimization Algorithms Research #hep-th
paper · pdf · doi:10.48550/arxiv.1802.04202
37 pages; dedicated to the memory of L.D.Faddeev, to be published by World Scientific; v2. refs added, typos fixed, discussion added, new solutions in 1+1 and 3+1 are announced; v3 refs added, typos fixed
openalex publication_date 2018/02/12 · arxiv created 2020/04/03 · arxiv updated 2020/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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+ years old approach by finding the honest solutions of equations of motion of the complexified classical mechanical system. These ideas originate 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 Ω-deformed B-model. We propose the notion of the topological renormalization group.