Non-Abelian Gerbes with Connections in Higher Gauge Theory

Explore the advanced mathematical concepts of non-Abelian gerbes with connections in higher gauge theory in this 2-hour 39-minute lecture from the Dublin Institute for Advanced Studies. Delve into the role of higher forms as gauge potentials in physics, focusing on the Kalb–Ramond B-field in string theory and supergravity. Examine the mathematical framework of categorified principal bundles and gerbes, contrasting well-established Abelian cases with the more complex non-Abelian scenarios. Learn about the challenges in defining connections on non-Abelian gerbes and the topological construction process. Discover the application of these concepts through the example of lifting an instanton--anti-instanton pair to a string 2-group bundle, and understand the potential significance of string structures in M5-brane dynamics.