G-flux and Spectral Divisors

TL;DR

This paper introduces a method for constructing G-flux in singular elliptic Calabi-Yau fourfolds within F-theory, utilizing spectral divisors that connect global geometry with local spectral cover descriptions.

Contribution

It presents a novel construction of G-flux using spectral divisors in resolved Calabi-Yau fourfolds, bridging global and local spectral cover approaches.

Findings

Constructed resolved geometry for E_6 singularity

Demonstrated equivalence of spectral divisor flux with direct flux construction

Reduced spectral divisor flux to spectral cover flux in the local limit

Abstract

We propose a construction of G-flux in singular elliptic Calabi-Yau fourfold compactifications of F-theory, which in the local limit allow a spectral cover description. The main tool of construction is the so-called spectral divisor in the resolved Calabi-Yau geometry, which in the local limit reduces to the Higgs bundle spectral cover. We exemplify the workings of this in the case of an E_6 singularity by constructing the resolved geometry, the spectral divisor and in the local limit, the spectral cover. The G-flux constructed with the spectral divisor is shown to be equivalent to the direct construction from suitably quantized linear combinations of holomorphic surfaces in the resolved geometry, and in the local limit reduces to the spectral cover flux.