Perturbative--nonperturbative connection in quantum mechanics and field theory

TL;DR

This paper reviews the intricate relationship between perturbative and nonperturbative physics across quantum mechanics and field theory, highlighting Arkady Vainshtein's contributions and discussing a duality in a special quantum system.

Contribution

It provides a comprehensive overview of the perturbative-nonperturbative connection, including a novel example of duality in a quasi-exactly solvable model independent of supersymmetry.

Findings

Explicit duality between perturbative and nonperturbative sectors in a quantum model

Connection between perturbative expansions and operator product expansions in field theory

Historical review of perturbative-nonperturbative relations in quantum mechanics

Abstract

On the occasion of this ArkadyFest, celebrating Arkady Vainshtein's 60th birthday, I review some selected aspects of the connection between perturbative and nonperturbative physics, a subject to which Arkady has made many important contributions. I first review this connection in quantum mechanics, which was the subject of Arkady's very first paper. Then I discuss this issue in relation to effective actions in field theory, which also touches on Arkady's work on operator product expansions. Finally, I conclude with a discussion of a special quantum mechanical system, a quasi-exactly solvable model with energy-reflection duality, which exhibits an explicit duality between the perturbative and nonperturbative sectors, without invoking supersymmetry.