$G_4$ Flux, Algebraic Cycles and Complex Structure Moduli Stabilization

Abstract

We construct $G_4$ fluxes that stabilize all of the 426 complex structure moduli of the sextic Calabi-Yau fourfold at the Fermat point. Studying flux stabilization usually requires solving Picard-Fuchs equations, which becomes unfeasible for models with many moduli. Here, we instead start by considering a specific point in the complex structure moduli space, and look for a flux that fixes us there. We show how to construct such fluxes by using algebraic cycles and analyze flat directions. This is discussed in detail for the sextic Calabi-Yau fourfold at the Fermat point, and we observe that there appears to be tension between M2-tadpole cancellation and the requirement of stabilizing all moduli. Finally, we apply our results to show that even though symmetric fluxes allow to automatically solve most of the F-term equations, they typically lead to flat directions.

35 pages

References in corpus (4)

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• Fixing D7 Brane Positions by F-Theory Fluxes
• Families of Quintic Calabi-Yau 3-Folds with Discrete Symmetries
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Cited by in corpus (15)

• The Tadpole Problem
• F-theory flux vacua at large complex structure
• On de Sitter String Vacua from Anti-D3-Branes in the Large Volume Scenario
• The tadpole conjecture at large complex-structure
• Effective Theory of Warped Compactifications and the Implications for KKLT
• Fluxes, Vacua, and Tadpoles meet Landau-Ginzburg and Fermat
• Moduli stabilization in type IIB orientifolds at $h^{2,1}=50$
• Moduli stabilization with non-geometric fluxes -- comments on tadpole contributions and de-Sitter vacua
• Remarks on the effects of quantum corrections on moduli stabilization and de Sitter vacua in type IIB string theory
• Universal Class of Type-IIB Flux Vacua with Analytic Mass Spectrum
• Fully stabilized Minkowski vacua in the $2^6$ Landau-Ginzburg model
• Stabilizing massless fields with fluxes in Landau-Ginzburg models
• Tadpole conjecture in non-geometric backgrounds
• Heterotic Complex Structure Moduli Stabilization for Elliptically Fibered Calabi-Yau Manifolds
• A Database of Calabi-Yau Orientifolds and the Size of D3-Tadpoles