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Heterotic M‐Theory, Warped Geometry and the Cosmological Constant Problem
Author(s) -
Krause Axel
Publication year - 2001
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/1521-3978(200102)49:1/3<163::aid-prop163>3.0.co;2-8
Subject(s) - heterotic string theory , physics , orbifold , cosmological constant , f theory , string theory , cosmological constant problem , compactification (mathematics) , theoretical physics , constant curvature , m theory , string (physics) , curvature , supergravity , geometry , mathematical physics , supersymmetry , quantum mechanics , mathematics , pure mathematics , dark energy , cosmology
Abstract The first part of this thesis analyzes whether a locally flat background represents a stable vacuum for the proposed heterotic M‐theory. A calculation of the leading order supergravity exchange diagrams leads to the conclusion that the locally flat vacuum cannot be stable. Afterwards a 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 a 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 2 l ≃ 1/ 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.