Yang–Mills theory for multiplicative Ehresmann connections

par Zan Grad (Leuven)

vendredi 6 nov. 2026, 14:00 → 15:00 Europe/Paris

112 (Bat. Braconnier)

Yang–Mills theory is a framework for finding connections with minimal curvature, using variational calculus. This talk is about a generalization of Yang–Mills theory, from principal bundles (viewed as transitive groupoids) to possibly non-transitive Lie groupoids and Lie algebroids. In our framework, principal bundle connections are replaced with the more general notion of (infinitesimal) multiplicative Ehresmann connections, which are a type of connections compatible with the structure of a Lie groupoid (or algebroid) introduced by Fernandes & Mărcuţ. Our action functional for such connections includes a curvature 3-form contribution, alongside the usual curvature 2-form term, and the resulting variational problem is naturally constrained by a cohomological condition. We present the associated Euler–Lagrange equations, demonstrate the gauge invariance of the solution space, and relate the global and infinitesimal theory via the van Est map. As an important application, we obtain a Yang–Mills theory for bundle gerbes.