Testing Stability of M-Theory on an S¹/Z₂ Orbifold

We analyse perturbatively, whether a flat background with vanishing G-flux in Horava-Witten supergravity represents a vacuum state, which is stable with respect to interactions between the ten-dimensional boundaries, mediated through the D=11 supergravity bulk fields. For this, we consider fluctuations in the graviton, gravitino and 3-form around the flat background, which couple to the boundary $E_8$ gauge-supermultiplet. They give rise to exchange amplitudes or forces between both boundary fixed-planes. In leading order of the D=11 gravitational coupling constant $\kappa$, we find an expected trivial vanishing of all three amplitudes and thereby stability of the flat vacuum in the static limit, in which the centre-of-mass energy $\sqrt{s}$ of the gauge-multiplet fields is zero. For $\sqrt{s}>0$, however, which could be regarded a vacuum state with excitations on the boundary, the amplitudes neither vanish nor cancel each other, thus leading to an attractive force between the fixed-planes in the flat vacuum. A ground state showing stability with regard to boundary excitations, is therefore expected to exhibit a non-trivial metric. Ten-dimensional Lorentz-invariance requires a warped geometry. Finally, we extrapolate the amplitudes to the case of coinciding boundaries and compare them to the ones resulting from the weakly coupled $E_8 \times E_8$ heterotic string theory at low energies.