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Topics in String Duality: D-Branes and Geometry

Abstract

One of the most striking and surprising aspects of string theory is the vast web of string dualities which relates many seemingly distinct string backgrounds. In this dissertation, I explore several novel dualities between systems of D-branes and closed string flux compactifications. I use geometric transitions to analyze a variety of supersymmetry-breaking D-brane constructions. I additionally present an explanation of the Calabi-Yau fourfold geometries which appear in the computation of superpotentials for D-branes on compact Calabi-Yau threefolds.

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