Topological properties of gauge theories and their applications to high-energy and condensed-matter physics

Abstract

Many remarkable properties of gauge theories rely on the topology of field configurations and/or ambient spacetime and are connected with quantum anomalies and nonperturbative excitations. These often exact properties have many implications on the physics of fundamental interactions, condensed matter systems and statistical mechanics models. They also account for a large part of the investigations in string theory and, combined with supersymmetry, have led to exact solutions of low-energy theories and the discovery of duality relations between supersymmetric gauge theories. The goal of this GGI activity has been that of bringing together theoreticians from different backgrounds, in condensed matter, high energy and mathematical physics, and encouraging discussion and collaboration.