Abstract
The Swampland Distance Conjecture suggests that an infinite tower of modes becomes exponentially light when approaching a point that is at infinite proper distance in field space. In this paper we investigate this conjecture in the Kähler moduli spaces of Calabi-Yau threefold compactifications and further elucidate the proposal that the infinite tower of states is generated by the discrete symmetries associated to infinite distance points. In the large volume regime the infinite tower of states is generated by the action of the local monodromy matrices and encoded by an orbit of D-brane charges. We express these monodromy matrices in terms of the triple intersection numbers to classify the infinite distance points and construct the associated infinite charge orbits that become massless. We then turn to a detailed study of charge orbits in elliptically fibered Calabi-Yau threefolds. We argue that for these geometries the modular symmetry in the moduli space can be used to transfer the large volume orbits to the small elliptic fiber regime. The resulting orbits can be used in compactifications of M-theory that are dual to F-theory compactifications including an additional circle. In particular, we show that there are always charge orbits satisfying the distance conjecture that correspond to Kaluza-Klein towers along that circle. Integrating out the KK towers yields an infinite distance in the moduli space thereby supporting the idea of emergence in that context.
Highlights
An upper bound on the scalar field range that any effective theory can accommodate in terms of the energy scale up to which the effective theory is valid
In this paper we investigate this conjecture in the Kahler moduli spaces of Calabi-Yau threefold compactifications and further elucidate the proposal that the infinite tower of states is generated by the discrete symmetries associated to infinite distance points
In this paper we have investigated the Swampland Distance Conjecture, and the associated notion of emergence of infinite field distances, in the context of Kahler moduli spaces of Calabi-Yau manifolds
Summary
In the following we will describe in more detail the above two proposals and present a new computation that shows how the exponential mass behavior (and the infinite field distance) is an automatic consequence of integrating out any infinite tower of states (regardless their concrete mass) up to the species bound of the tower, as long as the tower gets compressed as we move in the moduli space. If the number of species increases when approaching a point of the moduli space, quantum corrections from this tower will automatically generate a logarithmic field distance divergence in terms of the mass of these states. It could either be that the infinite tower generates part of the infinite field distance, a classical divergence being present, or that the infinite field distance fully emerges from quantum corrections form integrating out the tower In the latter case, the fact that moduli spaces are in general non-compact would be an IR effect from integrating out infinite towers of states that become massless at particular points. Even if the moduli space is not complex, as M-theory on a Calabi-Yau threefold or the circle compactification of F-theory, it will still be possible to have a notion of a monodromy transformation which will generate the tower and will correspond to some p-form discrete shift symmetry in the effective theory. It would be interesting to further investigate this relation between the SDC and generalized global symmetries in the future
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