Heterotic M-theory, warped geometry and the cosmological constant problem

The first part of this thesis analyzes whether a locally fiat background represents a stable vacuum for the proposed hererotic M-theory. A calculation of the leading order supergravity exchange diagrams leads to the conclusion that the locally flat vacuum cannot be stable. Afterwards 3 comparison with the corresponding weakly coupled heterotic string amplitudes is made, Next, we consider compactifications of heterotic M-theory on a Calabi-Yau threefold, including a non-vanishing G-flux. The ensuing warped-geometry is determined completely and used to show that the variation of the Calabi-Yau volume along the orbifold direction varies quadratically with distance instead linearly as suggested by an earlier first order approximation. In the second part of this thesis we propose 3 mechanism for obtaining a small cosmological constant. This mechanism consists of the separation of two domain-walls, which together constitute our world, up to a distance 21 similar or equal to1/M-GUT. The resulting warped-geometry leads to an exponential suppression of the cosmological constant, which thereby can obtain its observed value without introducing a large hierarchy. An embedding of this set-up into IIB string theory entails an SU(6) Grand Unified Theory with a natural explanation of the Higgs doublet-triplet splitting. Finally, we examine to what extent the string-theory T-duality can influence curvature. To this aim we derive the full transformation of the curvature-tensor under T-duality.