Integrability structures in string theory

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.

On 10 dimensional Exceptional Drinfel'd Algebras

“…There is no analogous statement for 3d sigma-models describing membranes propagating on 11d supergravity backgrounds. However, such defined generalized Yang-Baxter deformations are of certain interest (see [45] for a review).…”