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.Comment: 59 pages, v2: references added, typos correcte
