Topics in Five Dimensional Supersymmetry and Topological Quantum Field Theories

Sammanfattning: We explore five-dimensional supersymmetric quantum field theories and topological quantum field theories. In five dimensions, we describe a framework to consistently define a supersymmetric theory on a curved spacetime manifold. This is the starting point for the so called supersymmetric localization procedure which we exploit to compute the partition function on a large class of five-dimensional backgrounds. We discuss the geometric structure behind our result and analyze various extension of this program. Next, we present a seven-dimensional bulk topological field theory of abelian three-form potentials with a single derivative Chern-Simons-like action. We show how the edge modes can be understood from the perspective of a six-dimensional generalization of the fractional quantum Hall effect and compute an analog of the Laughlin wavefunction. We also explain why this has interesting implications for the study of six-dimensional superconformal field theories. Finally, we review a new approach to integrable lattice models in 1+1 dimensions based on a four-dimensional Chern-Simons-like theory and propose a strategy for its string theory embedding.