Non-perturbative String Theory from Water Waves

TL;DR

This paper develops non-perturbative solutions for exactly solvable string theories using a combined 't Hooft limit and numerical methods, revealing smooth connections between different asymptotic regimes and uncovering new theories.

Contribution

It introduces a novel approach to find non-perturbative solutions in string theory by linking perturbative regimes through interpolating functions and extends the known hierarchy of string equations.

Findings

Connected perturbative solutions via smooth interpolating functions.

Discovered new non-perturbative extensions of existing string theories.

Identified potential new string theories not evident in perturbative analysis.

Abstract

We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of which were conjectured to be the type IIA and IIB string theories coupled to (4,4k-2) superconformal minimal models of type (A,D). Our present paper shows that these new theories have smooth non-perturbative extensions. We also find evidence for putative new string theories that were not apparent in the perturbative analysis.