Year: 2025
Type: preprint
Abstract: F-theory compactifications on elliptically fibered Calabi--Yau threefolds yield consistent six-dimensional $\mathcal{N}=(1,0)$ 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.
Source: arXiv (Cornell University)
Author: Cota, Cesar Fierro
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Sorbonne Université
OpenAlex ID: W7117155687