Testing stability of M-theory on an S-1 = Z(2) orbifold

We analyse perturbatively, whether a at 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 t hrough the D = 11 supergravity bulk fields. For this, we consider fluctuati ons in the graviton, gravitino and 3 form around the at background, which c ouple to the boundary E-8 gauge-supermultiplet. They give rise to exchange amplitudes or forces between both boundary fixed-planes. In leading order o f the D = 11 gravitational coupling constant kappa, we find an expected tri vial vanishing of all three amplitudes and thereby stability of the at vacu um in the static limit, in which the centre-of-mass energy roots of the gau ge-multiplet fields is zero. For roots > 0, however, which could be regarde d a vacuum state with excitations on the boundary, the amplitudes neither v anish nor cancel each other, thus leading to an attractive force between th e fixed-planes in the at vacuum. A ground state showing stability with rega rd to boundary excitations, is therefore expected to exhibit a non-trivial metric. Ten-dimensional Lorentz-invariance requires a warped geometry. Fina lly, we extrapolate the amplitudes to the case of coinciding boundaries and compare them to the ones resulting from the weakly coupled E-8 x E-8 heter otic string theory at low energies.