pp Wave Big Bangs: Matrix Strings and Shrinking Fuzzy Spheres

TL;DR

It is shown 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.

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.

Figures (4)

• Figure 1: The scaled size of a giant graviton as a function of the time $t$ for $A=1$.
• Figure 2: Same as Fig. \ref{['size']}, but with $A=0.01$. Extended to smaller times, the size appears to hit a zero and then rise rapidly as time is further decreased; however, this is a regime for which our numerical solution is unreliable.
• Figure 3: Similar to Fig. \ref{['size']}, with $A=1$, but initial conditions at an earlier time.
• Figure 4: Same as Fig. \ref{['earlysize']}, but with $A=0.01$.