Topics in the String Landscape and the Swampland

Abstract

Although string theory gives rise to an enormous landscape" of possible effective theories at low energies, there seem to be many effective theories that are incompatible with string theory. Such theories are said to reside in the swampland." In part I of this thesis, we characterize the landscape of superconformal field theories and little string theories in six dimensions. We will see that string theory serves as a powerful tool for classifying theories in six dimensions and studying their properties. We will highlight some surprising connections between these theories and group theory, and we will provide strong evidence for the a-theorem in six dimensions. In part II of this thesis, we attempt to delineate the landscape of four-dimensional theories from the swampland using the Weak Gravity Conjecture (WGC). We show that the WGC places interesting constraints on models of large-field axion inflation. We further attempt to identify the correct form of the WGC, finding counterexamples to some forms and providing strong evidence in favor of others.