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The \({\mathcal N}=1\) effective action of F-theory compactifications. (English) Zbl 1207.81120

Summary: The four-dimensional \({\mathcal N}=1\) 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 Kähler 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.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
44A15 Special integral transforms (Legendre, Hilbert, etc.)
58D27 Moduli problems for differential geometric structures
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