String Theory and Water Waves

TL;DR

This paper reveals how an integrable hierarchy, the dispersive water wave hierarchy, organizes and connects various minimal string theories non-perturbatively, highlighting the role of Painleve equations in this framework.

Contribution

It introduces a unified integrable systems framework embedding multiple minimal string theories, including new conjectures about type IIA and IIB backgrounds.

Findings

Embedding of type 0A and 0B minimal strings into the water wave hierarchy

Identification of Painleve IV as organizing string theory physics

Proposal of new string-like limits corresponding to type IIA and IIB theories

Abstract

We uncover a remarkable role that an infinite hierarchy of non-linear differential equations plays in organizing and connecting certain {hat c}<1 string theories non-perturbatively. We are able to embed the type 0A and 0B (A,A) minimal string theories into this single framework. The string theories arise as special limits of a rich system of equations underpinned by an integrable system known as the dispersive water wave hierarchy. We observe that there are several other string-like limits of the system, and conjecture that some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain how these and several string-like special points arise and are connected. In some cases, the framework endows the theories with a non-perturbative definition for the first time. Notably, we discover that the Painleve IV equation plays a key role in organizing the string theory physics, joining its siblings, Painleve I and II, whose roles have previously been identified in this minimal string context.