The Swampland Distance Conjecture for Calabi-Yau Fourfold Compactifications
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There are a multitude of conjectures about the difference between the space of string theory derivable QFTs – the Landscape – and its complement – the Swampland. One of them, the Swampland Distance Conjecture, states that, upon approaching infinite distance points in field space, an infinite tower of states becomes massless. We study the premise and conclusion of this conjecture for the complex structure moduli space of Calabi-Yau fourfolds. For analyzing infinite distance points we employ the technology of mixed Hodge structures and their Deligne diamonds. With this we are able to give the first known classification of infinite distance divisors for general fourfolds. Furthermore we supplement this with rules for how these divisors can intersect and form an infinite distance network in field space. Using the same technology, we are able to identify infinite towers of states becoming massless for a big class of such intersection patterns. This provides further evidence for the general Swampland Distance Conjecture.