Exact solutions to quantum field theories and integrable equations

TL;DR

This paper explores exact solutions in quantum field theories and integrable systems, highlighting their interconnectedness and presenting detailed examples of hydrodynamical type equations within this framework.

Contribution

It demonstrates how solutions to quantum string and gauge theories can be formulated using integrable systems, unifying various known solutions under a common approach.

Findings

Solutions to quantum field theories can be expressed via integrable systems.

Examples of hydrodynamical type equations are detailed.

All known solutions are partial solutions to a unified integrable systems problem.

Abstract

The exact solutions to quantum string and gauge field theories are discussed and their formulation in the framework of integrable systems is presented. In particular I consider in detail several examples of appearence of solutions to the first-order integrable equations of hydrodynamical type and stress that all known examples can be treated as partial solutions to the same problem in the theory of integrable systems.