pp Wave Big Bangs: Matrix Strings and Shrinking Fuzzy Spheres

TL;DR

This paper constructs pp wave solutions with null-like dilatons in string theory, formulates Matrix String Theory in these backgrounds, and demonstrates that fuzzy cylinders dynamically shrink into strings over time, modeling aspects of big bang cosmology.

Contribution

It introduces a new class of pp wave backgrounds with null-like dilatons and analyzes the dynamics of fuzzy cylinders in these settings, revealing their evolution into strings.

Findings

Fuzzy cylinders shrink into strings at late times.

Matrix String Theory can be formulated in these pp wave backgrounds.

The models serve as toy models for big bang cosmologies.

Abstract

We find pp wave solutions in string theory with null-like linear dilatons. These provide toy models of big bang cosmologies. We formulate Matrix String Theory in these backgrounds. Near the big bang ``singularity'', the string theory becomes strongly coupled but the Yang-Mills description of the matrix string is weakly coupled. The presence of a second length scale allows us to focus on a specific class of non-abelian configurations, viz. fuzzy cylinders, for a suitable regime of parameters. We show that, for a class of pp waves, fuzzy cylinders which start out big at early times dynamically shrink into usual strings at sufficiently late times.