F-theory fluxes, Chirality and Chern-Simons theories

TL;DR

This paper investigates the generation of chiral matter spectra in four-dimensional F-theory compactifications by analyzing M-theory fluxes, intersection theory, and one-loop corrections, providing explicit formulas and examples for specific gauge groups.

Contribution

It introduces a method to compute chiral spectra in F-theory using M-theory fluxes, intersection numbers, and effective curves, linking geometry to physical chirality.

Findings

Derived explicit chirality formulas from intersection data.

Connected M-theory fluxes to four-dimensional chiral matter.

Validated methods with SU(5) and SU(5)×U(1) examples.

Abstract

We study the charged chiral matter spectrum of four-dimensional F-theory compactifications on elliptically fibered Calabi-Yau fourfolds by using the dual M-theory description. A chiral spectrum can be induced by M-theory four-form flux on the fully resolved Calabi-Yau fourfold. In M-theory this flux yields three-dimensional Chern-Simons couplings in the Coulomb branch of the gauge theory. In the F-theory compactification on an additional circle these couplings are only generated by one-loop corrections with charged fermions running in the loop. This identification allows us to infer the net number of chiral matter fields of the four-dimensional effective theory. The chirality formulas can be evaluated by using the intersection numbers and the cones of effective curves of the resolved fourfolds. We argue that a study of the effective curves also allows to follow the resolution process at each co-dimension. To write simple chirality formulas we suggest to use the effective curves involved in the resolution process to determine the matter surfaces and to connect with the group theory at co-dimension two in the base. We exemplify our methods on examples with SU(5) and SU(5)xU(1) gauge group.