Title: Yang–Mills theory for multiplicative Ehresmann connections
Speaker: Žan Grad (Instituto Superior Técnico)
Abstract: Classical Yang–Mills theory is a theoretical cornerstone of elementary particle physics. Roughly speaking, it is an application of calculus of variations to the theory of principal bundles, seeking to minimize the norm of the curvature of principal bundle connections. In this talk, we present a broad generalization of this framework to Lie groupoids and Lie algebroids, where principal bundle connections are replaced with (infinitesimal) multiplicative Ehresmann connections. This extends the classical theory to the non-integrable and non-transitive setting, capturing the dynamics of gauge fields in both longitudinal and transverse directions relative to the (singular) orbit foliation. We will present several examples, highlight the novel phenomena in the theory, and discuss connections to other known generalizations.