Casimir Effect Between World-Branes in Heterotic M-Theory

TL;DR

This paper investigates a non-supersymmetric M-theory compactification involving brane-antibrane systems, calculates the Casimir energy, predicts instabilities, and explores the potential end states of the system.

Contribution

It introduces a novel non-supersymmetric $E_8\times\bar E_8$ compactification, computes the Casimir energy, and analyzes the system's stability and possible decay mechanisms.

Findings

Attractive Casimir force between boundaries.

Development of tachyonic instability at Planck-scale separation.

Possible annihilation via wormhole nucleation.

Abstract

We study a non-supersymmetric $E_8\times\bar E_8$ compactification of M-theory on $S^1/Z_2$, 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.