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G-flux in F-theory and algebraic cycles. (English) Zbl 1246.81223

Summary: We construct explicit \(G_{4}\) fluxes in F-theory compactifications. Our method relies on identifying algebraic cycles in the Weierstrass equation of elliptic Calabi-Yau fourfolds. We show how to compute the \(D3\)-brane tadpole and the induced chirality indices directly in F-theory. Whenever a weak coupling limit is available, we compare and successfully match our findings to the corresponding results in type IIB string theory. Finally, we present some generalizations of our results which hint at a unified description of the elliptic Calabi-Yau fourfold together with the four-form flux \(G_{4}\) as a coherent sheaf. In this description the close link between \(G_{4}\) fluxes and algebraic cycles is manifest.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
81V15 Weak interaction in quantum theory
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References:

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