Integrability as Effective Principle of Nonperturbative Field and String Theories

TL;DR

This paper explores how integrability serves as a fundamental principle enabling nonperturbative analysis in quantum field and string theories, highlighting recent progress and future prospects.

Contribution

It emphasizes the role of integrability as a guiding principle for nonperturbative formulations in quantum field and string theories, discussing recent developments and potential future directions.

Findings

Integrability structures underpin nonperturbative results.

Several key steps have advanced understanding of integrability in these theories.

Speculations on future developments in the field.

Abstract

One of the perspectives in modern quantum field and string theory is related with the attempts to go beyond the perturbation theory. It turns out that a key principle in the formulation of all known non-perturbative results is {\it integrability}, i.e. arising of the structures of completely integrable systems. I discuss several important steps in this direction and speculate on its further possible development.