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We analyse perturbatively, whether a flat background with vanishing G-flux inHorava-Witten supergravity represents a vacuum state, which is stable withrespect to interactions between the ten-dimensional boundaries, mediatedthrough the D=11 supergravity bulk fields. For this, we consider fluctuationsin the graviton, gravitino and 3-form around the flat background, which coupleto the boundary $E_8$ gauge-supermultiplet. They give rise to exchangeamplitudes or forces between both boundary fixed-planes. In leading order ofthe D=11 gravitational coupling constant $\kappa$, we find an expected trivialvanishing of all three amplitudes and thereby stability of the flat vacuum inthe static limit, in which the centre-of-mass energy $\sqrt{s}$ of thegauge-multiplet fields is zero. For $\sqrt{s}>0$, however, which could beregarded a vacuum state with excitations on the boundary, the amplitudesneither vanish nor cancel each other, thus leading to an attractive forcebetween the fixed-planes in the flat vacuum. A ground state showing stabilitywith regard to boundary excitations, is therefore expected to exhibit anon-trivial metric. Ten-dimensional Lorentz-invariance requires a warpedgeometry. Finally, we extrapolate the amplitudes to the case of coincidingboundaries and compare them to the ones resulting from the weakly coupled $E_8\times E_8$ heterotic string theory at low energies.Comment: 30 pages, 5 figures, several minor corrections and clarification

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

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