2014/02/17 by Andreas P. Braun, Andrés Collinucci, Andres Collinucci +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Calabi–Yau manifold #Codimension #Coupling (piping) #Diagonal #F-theory #Gauge theory #Geometry #Gravitational singularity #Homogeneous space #Homotopy and Cohomology in Algebraic Topology #Massless particle #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Pure mathematics #Quantum mechanics #Singularity #String theory #Theoretical physics #hep-th
paper · pdf · doi:10.1007/jhep07(2014)028
18 pages
arxiv created 2014/02/17 · openalex publication_date 2014/07/01 · arxiv updated 2015/06/18 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
U(1) gauge symmetries in F-theory are expected to manifest themselves as codimension three singularities of Calabi-Yau fourfolds. However, some of these are known to become massive at strong coupling via the Stückelberg mechanism. In this note, we propose a geometric picture for detecting all U(1)’s, and determining which ones are massive and which ones are massless. We find that massive gauge symmetries show up as codimension three singularities that only admit small, non-Kähler, resolutions. Our proposal passes several highly non-trivial tests, including a case with a non-diagonal mass matrix.