In this thesis we study several differential-geometric aspects of the low energy limit of string theory. We focus on anomaly cancellation issues in M-theory on a manifold with boundary and background fluxes, and the computation of non-holomorphic quantities in Calabi-Yau compactifications.
In the first chapter we introduce the motivation and the problems that we will study. In the second chapter we show how the coupling of gravitinos and gauginos to fluxes modifies anomaly cancellation in M-theory on a manifold with boundary. Anomaly cancellation continues to hold, after a shift of the definition of the gauge currents by a local gauge invariant expression in the curvatures and E8 fieldstrengths. We compute the first nontrivial correction of this kind. In the last chapter, we introduce methods to determine the form of the effective fourdimensional field theory corresponding to compactifications of string theory. More precisely, we develop iterative methods for finding solutions to the Ricci flat equations on a Calabi-Yau variety, and to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas developed by Donaldson. Finally, we show how these techniques can be understood using the language of geometric quantization of Kaehler manifolds, and suggest how one can use these ideas to explicitly construct additional geometric objects.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 86-92).
Subject (ID = SUBJ1); (authority = RUETD)
Topic
Physics and Astronomy
Subject (ID = SUBJ2); (authority = ETD-LCSH)
Topic
String models
Subject (ID = SUBJ3); (authority = ETD-LCSH)
Topic
Mathematical physics
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Graduate School - New Brunswick Electronic Theses and Dissertations
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Identifier (type = doi)
doi:10.7282/T3VM4CM6
Genre (authority = ExL-Esploro)
ETD doctoral
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Sergio Lukic
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Rutgers University. Graduate School - New Brunswick
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