Uploaded November 2023 | Updated September 2026, 2 weeks ago
Abstract: "Higher forms arise as gauge potentials in a number of contexts within physics. The prime example is the Kalb–Ramond B-field of string theory, which is found also in the low-energy supergravity limits. Mathematically, these gauge potentials are connections on higher or categorified principal bundles also known as gerbes. In the Abelian case, the theory of gerbes is well-established and used in many contexts. In this seminar, I will talk about how one can extend this theory to the non-Abelian setting. There, the situation is much more subtle. Although the topological construction of non-Abelian gerbes is relatively straightforward, defining a connection on such a gerbe requires much more work. After formulating the general construction, I will illustrate it by lifting the principal bundle corresponding to an instanton--anti-instanton pair to a string 2-group bundle. Such "string structures'' are believed to play a role in the dynamics of M5-branes."
Abstract: "Higher forms arise as gauge potentials in a number of contexts within physics. The prime example is the Kalb–Ramond B-field of string theory, which is found also in the low-energy supergravity limits. Mathematically, these gauge potentials are connections on higher or categorified principal bundles also known as gerbes. In the Abelian case, the theory of gerbes is well-established and used in many contexts. In this seminar, I will talk about how one can extend this theory to the non-Abelian setting. There, the situation is much more subtle. Although the topological construction of non-Abelian gerbes is relatively straightforward, defining a connection on such a gerbe requires much more work. After formulating the general construction, I will illustrate it by lifting the principal bundle corresponding to an instanton--anti-instanton pair to a string 2-group bundle. Such "string structures'' are believed to play a role in the dynamics of M5-branes."
