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

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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 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 E₈ × E₈ heterotic string theory at low energies.