Yukawas, G-flux, and Spectral Covers from Resolved Calabi-Yau's

TL;DR

The paper provides a global resolution framework for elliptically fibered Calabi–Yau fourfolds with an A4 surface, enabling explicit calculation of topological data and a rigorous link between global G-flux and local spectral-cover data. By performing the Esole–Yau resolution and computing c2 and χ, the authors prove an Euler-characteristic shift conjecture and construct fluxes that reproduce the local model spectrum and D3-tadpoles. They analyze codimension-2 and codimension-3 fibers to elucidate the emergence of Yukawa couplings via SU(5) weight lattices, showing how Yukawas arise without rank enhancement. The work also establishes a concrete connection between global G-flux data and the spectral-divisor/Higgs-cover formalism, demonstrating how the local spectral cover emerges from the resolved Calabi–Yau geometry and aligning quantization rules across local and global pictures.

Abstract

We use the resolution procedure of Esole and Yau arXiv:1107.0733 to study Yukawa couplings, G-flux, and the emergence of spectral covers from elliptically fibered Calabi-Yau's with a surface of A_4 singularities. We provide a global description of the Esole-Yau resolution and use it to explicitly compute Chern classes of the resolved 4-fold, proving the conjecture of arXiv:0908.1784 for the Euler character in the process. We comment on the physical implications of the surprising singular fibers in codimension 2 and 3 in arXiv:1107.0733 and emphasize a group theoretic interpretation based on the A_4 weight lattice. We then construct explicit G-fluxes by brute force in one of the 6 birationally equivalent Esole-Yau resolutions, quantize them explicitly using our result for the second Chern class, and compute the spectrum and flux-induced 3-brane charges, finding agreement with results and conjectures of local models in all cases. Finally, we provide a precise description of the spectral divisor formalism in this setting and sharpen the procedure described in arXiv:1107.1718 in order to explicitly demonstrate how the Higgs bundle spectral cover of the local model emerges from the resolved Calabi-Yau geometry. Along the way, we demonstrate explicitly how the quantization rules for fluxes in the local and global models are related.