Mathematics – Logic
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008phdt........34j&link_type=abstract
ProQuest Dissertations And Theses; Thesis (Ph.D.)--Columbia University, 2008.; Publication Number: AAT3317568; ISBN: 97805496567
Mathematics
Logic
Scientific paper
String theory is the most promising framework for uniting quantum mechanics and gravity into a single consistent system. But formidable obstacles remain in the attempt to relate it to observations. The crux of many of the problems is that the solutions with 4 large space-time dimensions and the phenomenologically desirable N = 1 supersymmetry (compactifications on Calabi-Yau 3-folds) typically contain a large number of moduli - scalar fields with exactly flat potentials, which are incompatible with our understanding of the early universe. One of the most popular suggestions for resolving the issue is to give the moduli masses by adding fluxes around cycles in the Calabi-Yau manifold. This results in a contribution to the superpotential proportional to the periods of the holomorphic 3-form, which are in general very difficult to calculate. We present a method for finding the periods in certain cases with discrete symmetries, that has applications both to the physics of string compactification, and to the mathematics of mirror symmetry. We then examine another mechanism for giving the moduli masses which arises near points in moduli space where extra massless species appear. We find interesting chaotic behavior near such points suggesting that the effect of the classical potential is less helpful than previously believed. Including quantum particle production in the analysis is then seen to yield a more satisfactory way to generate masses. Finally we consider a possibly beneficial consequence of light scalar fields in the early universe. Since string theory contains no dimensionless parameters, the values of all coupling constants are determined by vacuum expectation values of scalar fields. The flat potentials might have allowed the moduli controlling the strength of gravity to vary, resulting in a period of time in the early universe when gravity was much weaker than it is now. As a small step in the study of such models, we analyze the implications for the origin of the arrow of time.
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