Casimir Effect Between World-Branes in Heterotic M-Theory

We study a non-supersymmetric $E_8\times {\bar{E}}_8$ compactification of M-theory on $S^1\mathrm{/}{Z}_2$, related to the supersymmetric $E_8\times E_8$ theory by a chirality flip at one of the boundaries. This system represents an M-theory analog of the D-brane anti-D-brane systems of string theory. Alternatively, this compactification can be viewed as a model of supersymmetry breaking in the ``brane-world’’ approach to phenomenology. We calculate the Casimir energy of the system at large separations, and show that there is an attractive Casimir force between the $E_8$ and ${\bar{E}}_8$ boundary. We predict that a tachyonic instability develops at separations of order the Planck scale, and discuss the possibility that the M-theory fivebrane might appear as a topological defect supported by the $E_8\times {\bar{E}}_8$ system. Finally, we analyze the eventual fate of the configuration, in the semiclassical approximation at large separations: the two ends of the world annihilate by nucleating wormholes between the two boundaries.