Testing stability of M-theory on an S1/Z2-orbifold

We analyse perturbatively, whether a flat background with vanishing G-flux in 't Hooft-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 E8 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 κ, 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 √{s} of the gauge-multiplet fields is zero. For √{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 E8xE8 heterotic string theory at low energies. (author)