Abstract
We propose a combined mechanism to realize both winding inflation and de Sitter uplifts. We realize the necessary structure of competing terms in the scalar potential not via tuning the vacuum expectation values of the complex structure moduli, but by a hierarchy of the Gopakumar-Vafa invariants of the underlying Calabi-Yau threefold. To show that Calabi-Yau threefolds with the prescribed hierarchy actually exist, we explicitly create a database of all the genus 0 Gopakumar-Vafa invariants up to total degree 10 for all the complete intersection Calabi-Yau’s up to Picard number 9. As a side product, we also identify all the redundancies present in the CICY list, up to Picard number 13. Both databases can be accessed at this link (https://www.desy.de/∼westphal/GV_CICY_webpage/GVInvariants.html).
Highlights
JHEP05(2021)271 encoded by the GV invariants can provide a controlled lifting of flat directions left over in the complex structure (c.s.) moduli space by properly choosing fluxes in type IIB string theory CY orientifold flux compactifications [9, 10]
[9] shows that properly choosing the fluxes can generate flat axion valleys with a large path length on a small fundamental domain, which allows to generate inflationary dynamics once the long flat valley is lifted by the GV-controlled instanton effects. Based on these literature results, we show in this paper that having a large database of CYs with known GV invariants in hand, we can use CYs with a built-in hierarchy of the lowest-degree GV invariants to collaborate with the tuning of c.s. moduli VEV hierarchies in controlling the instanton contributions to the scalar potential, and in some cases remove the need to tune hierarchical c.s
Without reviewing the full discussion of either KKLT-type [11,12,13] or Large Volume Scenario (LVS) [14] type stabilization of the Kähler moduli forming the lightest moduli sector, their respective requirements of either a full set of h1,1 rigid 4-cycles or a CY with h1,1 < h2,1 imply that our explicit examples of this paper show the existence of the ingredients intrinsic to the uplift/inflation sector itself but they cannot be made to work as full examples in particular in the context of LVS
Summary
In [9], the authors present a model of large field inflation for a Calabi-Yau orientifold X compactification of type IIB superstring theory. As long as the dynamics of winding inflation or winding uplifts is realized using stabilized c.s. values at moderately large complex structure (corresponding to c.s. moduli VEVs Im zi O(1)), the extended no-scale structure of the string loop corrections ensures that, already for quite moderate values of the stabilized volume V, the induced scalar potential terms are subdominant to any parts of V induced from fluxes, non-perturbative corrections and/or α -corrections used for moduli stabilization and the winding c.s. axion dynamics in e.g. the KKLT or LVS scenarios Provided these conditions are satisfied we can neglect the string loop corrections which would spoil the factorization of the moduli space. The terms of the c.s. axion winding scalar potential are controlled by the GV invariants and the VEVs of the c.s. moduli These VEVs were determined by the 3-form flux scalar potential and receive only suppressed corrections from the stress-energy sources driving Kähler moduli stabilization by virtue of the above hierarchies.
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