This Wednesday (16 October 15:00 B404) we have the Mathematical and Theoretical Physics Seminar by Mehran Jalali Farahani from Heriot-Watt University. In addition, Mehran will also give a pre-talk at 14:00 D450, intended to be accessible to MSc and early PhD students, giving some background for the main seminar talk. After the main seminar, there will be tea and refreshments on Spectra 3rd floor Connect Area.
Mehran will talk about general gauge theories with a scalar field and a vector field. When there is only a scalar field (nonlinear sigma model), the scalar field takes values in a manifold; when there is only a vector field (Yang–Mills theory), the vector field takes values in (a connection on a principal bundle for) a Lie group; when both are present, the manifold and the Lie group combine into a more general structure known as a Lie groupoid, which has many applications across physics and mathematics.
Title:Principal Lie groupoid bundles with connection (and a bit beyond)
Abstract: In this talk, I present our recent work towards general theory of higher principal bundles with connection. In particular, we developed the notion of principal groupoid‐bundles with connection using a new framework that is suitable for generalization. In this setup, principal bundles with connection are principal bundles without connection in a different category, namely the category of NQ‐manifolds.