| Summary: | Chapter 3 reviews anomalies in field theories and the anomaly inflow mechanism in space-filling intersecting brane configurations. We review and discuss dynamics at the intersection domain of the <i>I</i>1 system (whose intersection domain is (1 + 1)-dimensional). We also present a supergravity solution of intersecting <i>D7</i>-branes over (5 + 1) dimensions i.e. the <i>I</i>5 system, and discuss their connections to the conifold in F-theory. Chapter 4 is concerned with the study of entropies of small black holes in IIB string theory, in the presence of higher derivative corrections. In chapter 5 we study <i>D</i>-brane inflation in the warped throat, where a <i>D</i>3-brane open-string modulus plays the role of the inflation. We review the computation of non-perturbative corrections to the inflation potential from holomorphically-embedded stacks of <i>D7-</i>branes, and derive explicit expressions for the case of two non-intersecting sets of Kuperstein embedded <i>D7</i>’s. We present explicit models that satisfies <i>angular stability</i>, and demonstrate how models with an inflation scale exceeding that of SUSY breaking are constructed.
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