# Non-perturbative String Theory from Water Waves

## 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.

- Authors:

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1043194

- Report Number(s):
- SLAC-PUB-15088

Journal ID: ISSN 1751-8121; arXiv:1011.6354; TRN: US201213%%131

- DOE Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Physics. A, Mathematical and Theoretical (Online)

- Additional Journal Information:
- Journal Volume: 44; Journal Issue: 37; Journal ID: ISSN 1751-8121

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIFFERENTIAL EQUATIONS; PERTURBATION THEORY; STRING THEORY; WATER WAVES; HEPTH

### Citation Formats

```
Iyer, Ramakrishnan, Johnson, Clifford V., /Southern California U., Pennington, Jeffrey S., and /SLAC.
```*Non-perturbative String Theory from Water Waves*. United States: N. p., 2012.
Web.

```
Iyer, Ramakrishnan, Johnson, Clifford V., /Southern California U., Pennington, Jeffrey S., & /SLAC.
```*Non-perturbative String Theory from Water Waves*. United States.

```
Iyer, Ramakrishnan, Johnson, Clifford V., /Southern California U., Pennington, Jeffrey S., and /SLAC. Thu .
"Non-perturbative String Theory from Water Waves". United States. https://www.osti.gov/servlets/purl/1043194.
```

```
@article{osti_1043194,
```

title = {Non-perturbative String Theory from Water Waves},

author = {Iyer, Ramakrishnan and Johnson, Clifford V. and /Southern California U. and Pennington, Jeffrey S. and /SLAC},

abstractNote = {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.},

doi = {},

journal = {Journal of Physics. A, Mathematical and Theoretical (Online)},

issn = {1751-8121},

number = 37,

volume = 44,

place = {United States},

year = {2012},

month = {6}

}