Abstract
We argue that in type IIB LVS string models, after including the leading order moduli stabilisation effects, the moduli space for the remaining flat directions is compact due the Calabi-Yau Kähler cone conditions. In cosmological applications, this gives an inflaton field range which is bounded from above, in analogy with recent results from the weak gravity and swampland conjectures. We support our claim by explicitly showing that it holds for all LVS vacua with h1,1 = 3 obtained from 4-dimensional reflexive polytopes. In particular, we first search for all Calabi-Yau threefolds from the Kreuzer-Skarke list with h1,1 = 2, 3 and 4 which allow for LVS vacua, finding several new LVS geometries which were so far unknown. We then focus on the h1,1 = 3 cases and show that the Kähler cones of all toric hypersurface threefolds force the effective 1-dimensional LVS moduli space to be compact. We find that the moduli space size can generically be trans-Planckian only for K3 fibred examples.
Highlights
We address this question in a particular class of vacua, namely for the moduli space of Kahler deformations in the context of type IIB Calabi-Yau (CY) orientifold compactifications with background fluxes
We argue that in type IIB Large Volume Scenario (LVS) string models, after including the leading order moduli stabilisation effects, the moduli space for the remaining flat directions is compact due the Calabi-Yau Kahler cone conditions
We turn to the explicit scan for LVS vacua which, according to the discussion in section 2, we identify with CY geometries with diagonal del Pezzo (dP) divisors
Summary
We first review the necessary ingredients for the realisation of LVS vacua which feature a reduced moduli space after leading order moduli stabilisation.
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