String theory and classical integrable systems

TL;DR

This paper explores the connections between string theory, 2D quantum gravity, and classical integrable systems, highlighting different formulations and potential generalizations to higher dimensions and quantum integrability.

Contribution

It demonstrates how classical integrable systems naturally emerge in string theory through various formulations, and discusses potential extensions to quantum integrable structures.

Findings

Classical integrable systems appear in string theory formulations.

Different approaches to string theory unify multiple vacua descriptions.

Speculations on quantum integrable structures in string theory.

Abstract

We discuss different formulations and approaches to string theory and $ 2d$ quantum gravity. The generic idea to get a unique description of {\it many} different string vacua altogether is demonstrated on the examples in $ 2d$ conformal, topological and matrix formulations. The last one naturally brings us to the appearance of classical integrable systems in string theory. Physical meaning of the appearing structures is discussed and some attempts to find directions of possible generalizations to ``higher-dimensional" models are made. We also speculate on the possible appearence of quantum integrable structures in string theory.