2024/06/24 by S. Fischer, Mehran Jalali Farahani, Fischer, Simon-Raphael +5 · 2 citations
Mathematics · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2406.16755
openalex publication_date 2024/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a new perspective on principal bundles with connection as morphisms from the tangent bundle of the underlying manifold to a classifying dg-Lie groupoid. This groupoid can be identified with a lift of the inner homomorphisms groupoid arising in Ševera's differentiation procedure of Lie quasi-groupoids. Our new perspective readily extends to principal groupoid bundles, but requires an adjustment, an additional datum familiar from higher gauge theory. We show that for Lie groupoids, the additional adjustment data amounts to a Cartan connection. The resulting adjusted connections naturally provide a global formulation of the kinematical data of curved Yang-Mills-Higgs theories as described by Kotov-Strobl (arXiv:1510.07654) and Fischer (arXiv:2104.02175).