2025/12/20 by Cesar Fierro Cota, Cota, Cesar Fierro
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.48550/arxiv.2512.18151
openalex publication_date 2025/12/20 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28
F-theory compactifications on elliptically fibered Calabi--Yau threefolds yield consistent six-dimensional N=(1,0) supergravity theories, for which the cancellation of gravitational, gauge and mixed anomalies imposes non-trivial algebraic relations between classical intersection data and enumerative geometry invariants of curves in the fiber. In this work, we capture the spectrum of such theories via meromorphic quasi-Jacobi forms of index zero whose Fourier coefficients determine the genus zero Gromov--Witten theory restricted to curve classes in the fiber. We find that the one-loop anomaly coefficients of the effective six-dimensional theories are encoded in the modular properties of these automorphic forms, while the Green--Schwarz counterterms are made manifest by the Fourier--Mukai transform action on zero- and two-branes associated with double T-duality along the elliptic fiber. Moreover, we show that the anomaly cancellation conditions are automatically satisfied in this class of string compactifications as a consequence of the holomorphic anomaly equations of topological string theory.