Integrability structures in string theory

TL;DR

This review explores integrability structures in string theory, focusing on Nambu structures and loop variables in membrane dynamics, and discusses potential links to membrane integrability.

Contribution

It synthesizes various methods and observations related to three-dimensional integrability structures, highlighting connections and proposing future research directions.

Findings

Emphasizes the role of Nambu structures in membrane dynamics

Highlights the significance of loop variables in integrability

Speculates on the relation between membrane structures and integrability

Abstract

This review is a collection of various methods and observations relevant to structures in three-dimensional systems similar to those responsible for integrability of two-dimensional systems. Particular focus is given to Nambu structures and loop variables naturally appearing in membrane dynamics. While reviewing each topic in more details we emphasize connections between them and speculate on possible relations to membrane integrability.