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

TL;DR

This paper uses a resolution method to analyze Yukawa couplings, G-flux, and spectral covers in elliptically fibered Calabi-Yau manifolds, providing explicit computations and clarifying the geometric and physical implications.

Contribution

It offers a global resolution framework, computes Chern classes, constructs explicit G-fluxes, and connects local and global spectral cover formalisms in Calabi-Yau compactifications.

Findings

Proved the Euler characteristic conjecture for resolved Calabi-Yau four-folds.

Constructed explicit G-fluxes and matched flux-induced charges with local models.

Demonstrated the emergence of spectral covers from resolved geometries.

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.