Seminár Katedry teoretickej fyziky - Dominik Rist (15.6.2022)
v stredu 15.6.2022 o 14:00 hod. v miestnosti F2/125
Od: Peter Maták
Prednášajúci: Dominik Rist
Názov: Non-Abelian Gerbes with Connections (with a two-bundle of string quartets)
Termín: 15.6.2022, 14:00 hod., miestnosť F2/125
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 (one just lifts the cocycle relations for transition functions of an ordinary principal bundle to hold up to homotopies, which are then encoded in higher components of the cocycle), 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. This talk is based on our recent work arXiv:2203.00092.