2025/07/08 by Caucher Birkar, Seung-Joo Lee, Birkar, Caucher +1 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2507.06295
openalex publication_date 2025/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a novel strategy to derive explicit and uniform upper bounds on the particle spectrum of six-dimensional gravitational theories with minimal supersymmetry, focusing initially on the tensor sector. The strategy is motivated by considerations of F-theory compactifications on elliptic Calabi-Yau 3-folds. However, it admits a clear bottom-up interpretation and is thus applicable to general supergravity theories modulo certain physical conjectures. At the heart of the strategy are two key structures, most natural in birational geometry: one concerns the singularity of the natural pairs on the base manifolds, and the other, the fibration generically exhibited by the bases. Put physically, the former structure keeps the effective theories from decompactifying and the latter ensures the (generic) presence of a heterotic string. We sketch our bounding strategy and present, for an illustration, the explicit bounds thereby derived on the tensor spectrum, with the technical details relegated to a companion paper [1].