Swampland distance conjecture for one-parameter Calabi-Yau threefolds

Abstract

We investigate the swampland distance conjecture (SDC) in the complex moduli space of type II compactifications on one-parameter Calabi-Yau threefolds. This class of manifolds contains hundreds of examples and, in particular, a subset of 14 geometries with hypergeometric differential Picard-Fuchs operators. Of the four principal types of singularities that can occur -specified by their limiting mixed Hodge structure -only the K-points and the large radius points (or more generally the M -points) are at infinite distance and therefore of interest to the SDC. We argue that the conjecture is fulfilled at the K-and the M -points, including models with several M -points, using explicit calculations in hypergeometric models which contain typical examples of all these degenerations. Together with previous work on the large radius points, this suggests that the SDC is indeed fulfilled for one-parameter Calabi-Yau spaces.

The Swampland: Introduction and Review

“…Indeed, known moduli spaces span a vast spectrum, not least due to each Calabi‐Yau manifold supporting such a moduli space. Nonetheless, we will see that the structures of the distance conjectures can still be shown to arise within such moduli spaces . In particular, in [] a formalism was developed which allows to study infinite distances in moduli spaces with complete generality.…”

Refined swampland distance conjecture and exotic hybrid Calabi-Yaus

“…The latter case has been studied for instance in [22,33], where models of this type were named pseudohybrids. K-points are at infinite distance in the moduli space, and it has been argued in [15] that an infinite number of D-branes becomes massless, as expected by the SDC. K-points typically correspond to hybrid phases, which are described in terms of Landau-Ginzburg orbifolds fibered over some base manifold.…”

“…See for instance [34,35] for partial list and [36] for a full classification. The complete list has also recently been given in [15]. Three models within this class have C-type pseudo-hybrid phases, see table 2.…”

“…While this work was in preparation [15] appeared which also computes the metrics on M K for the examples we discuss, albeit with different methods.…”

Trans-Planckian censorship conjecture from the swampland distance conjecture

“…In a similar vein, we shall show that the TCC can be derived starting from a wellexplored aspect of quantum gravity -the SDC -assuming some scaling for the cut-off according to the species bound [59][60][61][62]. Since the SDC has been tested extensively in concrete examples coming from string theory (e.g., [47,48,[63][64][65][66][67]), our derivation makes the TCC much more robust, and consequently, its implications for cosmology more unavoidable. As an aside, it shall also demonstrate how the logarithmic corrections [1,68] naturally arise in the dS conjecture, starting from the SDC and using the species bound if one does not require that the field excursion |∆ϕ| → ∞.…”