The N=1 effective action of F-theory compactifications

TL;DR

This paper derives the four-dimensional N=1 effective action for F-theory compactifications on Calabi-Yau fourfolds, using M-theory lift, T-duality, and vector-scalar duality, including gauge couplings and matter interactions.

Contribution

It provides a detailed derivation of the effective action, including gauge couplings and matter couplings, by lifting M-theory compactifications and applying dualities, extending previous work on F-theory compactifications.

Findings

Determined the Kahler potential and gauge-kinetic functions.

Included gauge theories from seven-branes and R-R bulk sector.

Analyzed electromagnetic duality in the effective theory.

Abstract

The four-dimensional N=1 effective action of F-theory compactified on a Calabi-Yau fourfold is studied by lifting a three-dimensional M-theory compactification. The lift is performed by using T-duality realized via a Legendre transform on the level of the effective action, and the application of vector-scalar duality in three dimensions. The leading order Kahler potential and gauge-kinetic coupling functions are determined. In these compactifications two sources of gauge theories are present. Space-time filling non-Abelian seven-branes arise at the singularities of the elliptic fibration of the fourfold. Their couplings are included by resolving the singular fourfold. Generically a U(1)^r gauge theory arises from the R-R bulk sector if the base of the elliptically fibered Calabi-Yau fourfold supports 2r harmonic three-forms. The gauge coupling functions depend holomorphically on the complex structure moduli of the fourfold, comprising closed and open string degrees of freedom. The four-dimensional electro-magnetic duality is studied in the three-dimensional effective theory obtained after M-theory compactification. A discussion of matter couplings transforming in the adjoint of the seven-brane gauge group is included.