At large complex structure in F-theory, the F-term potential simplifies to V = Z^{AB} ρ_A ρ_B, yielding two families of flux vacua with all complex structure moduli fixed, one with bounded saxion vevs and one with unbounded vevs where N_flux factors into two integers.
Quantum periods of Calabi-Yau fourfolds
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abstract
In this work we study the quantum periods together with their Picard-Fuchs differential equations of Calabi-Yau fourfolds. In contrast to Calabi-Yau threefolds, we argue that the large volume points of Calabi-Yau fourfolds generically are regular singular points of the Picard-Fuchs operators of non-maximally unipotent monodromy. We demonstrate this property in explicit examples of Calabi-Yau fourfolds with a single Kahler modulus. For these examples we construct integral quantum periods and study their global properties in the quantum Kahler moduli space with the help of numerical analytic continuation techniques. Furthermore, we determine their genus zero Gromov-Witten invariants, their Klemm-Pandharipande meeting invariants, and their genus one BPS invariants. In our computations we emphasize the features attributed to the non-maximally unipotent monodromy property. For instance, it implies the existence of integral quantum periods that at large volume are purely worldsheet instanton generated. To verify our results, we also present intersection theory techniques to enumerate lines with a marked point on complete intersection Calabi-Yau fourfolds in Grassmannian varieties.
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Non-perturbative g_s corrections obstruct perturbative Type IIB descriptions and can remove classical infinite distance degenerations in asymptotic regions of the complex structure moduli space.
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F-theory flux vacua at large complex structure
At large complex structure in F-theory, the F-term potential simplifies to V = Z^{AB} ρ_A ρ_B, yielding two families of flux vacua with all complex structure moduli fixed, one with bounded saxion vevs and one with unbounded vevs where N_flux factors into two integers.
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Quantum obstructions for $N=1$ infinite distance limits -- Part I: $g_s$ obstructions
Non-perturbative g_s corrections obstruct perturbative Type IIB descriptions and can remove classical infinite distance degenerations in asymptotic regions of the complex structure moduli space.