The Swampland Distance Conjecture for Kahler moduli

TL;DR

<3-5 sentence high-level summary> The Swampland Distance Conjecture (SDC) is tested in the Kahler moduli spaces of Calabi–Yau threefolds, showing that infinite proper distance is accompanied by an infinite tower of states that becomes exponentially light. This tower is identified with a discrete monodromy‑generated charge orbit of BPS states, whose masslessness at infinite distance is controlled by log‑monodromy data tied to triple intersection numbers; in elliptic fibrations, modular symmetry transfers the orbit to the small fiber, enabling a dual M‑/F‑theory interpretation and a geometric realization of emergence from integrating out towers. The work develops a general large‑volume framework for classifying infinite distance loci (types II, III, IV) and constructing universal charge orbits (dominated by D2–D0 bound states in IIA), and shows how a Fourier–Mukai transform maps large‑volume orbits to small‑fiber regimes, effectively realizing KK towers in the F‑theory limit. Together these results reinforce the view that infinite distances signal a breakdown of effective field theory due to quantum gravity constraints and demonstrate emergence as a mechanism linking topology, dualities, and light towers within string theory.

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.

Figures (1)

• Figure 1: The large volume regime is related to the small fiber regime by a double T-duality along the elliptic fiber. This duality is implemented by a Fourier-Mukai transform.