Colliding branes in heterotic M theory

Abstract

We study the collision of two flat, parallel end-of-the-world branes in heterotic M theory. By insisting that there is no divergence in the Riemann curvature as the collision approaches, we are able to single out a unique solution possessing the local geometry of (2d compactified Milne)/${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{R}}_{3}$, times a finite-volume Calabi-Yau manifold in the vicinity of the collision. At a finite time before and after the collision, a second type of singularity appears momentarily on the negative-tension brane, representing its bouncing off a zero of the bulk warp factor. We find this singularity to be remarkably mild and easily regularized. The various different cosmological solutions to heterotic M theory previously found by other authors are shown to merely represent different portions of a unique flat cosmological solution to heterotic M theory.