Multiple Fibrations in Calabi-Yau Geometry and String Dualities

TL;DR

The paper investigates Calabi–Yau n-folds with multiple fibrations and analyzes how distinct F-theory vacua, arising from different elliptic or genus-one descriptions of the same total space, can converge to the same M-theory limit upon circle reduction and Coulomb-branch flow. It develops explicit geometric and field-theoretic tools to relate 6D F-theory spectra, 5D M-/F-theory limits, and heterotic/F-theory dualities across 8D, 6D, and 4D, including cases with non-Abelian, Abelian, and superconformal sectors via Mordell-Weil groups and nested fibrations. The study provides detailed examples of multiply-fibered CY3s yielding networks of dual theories, checks anomaly cancellation, and demonstrates how higher rank Mordell-Weil groups generate rich Abelian sectors while preserving a common 5D limit. It also extends these ideas to heterotic dualities, T-duality, and mirror symmetry, highlighting how nested and multiple fibrations encode dualities in lower dimensions and offering a framework to catalog dualities across CY datasets for future phenomenological and mathematical exploration.

Abstract

In this work we explore the physics associated to Calabi-Yau (CY) n-folds that can be described as a fibration in more than one way. Beginning with F-theory vacua in various dimensions, we consider limits/dualities with M-theory, type IIA, and heterotic string theories. Our results include many M-/F-theory correspondences in which distinct F-theory vacua - associated to different elliptic fibrations of the same CY n-fold - give rise to the same M-theory limit in one dimension lower. Examples include 5-dimensional correspondences between 6-dimensional theories with Abelian, non-Abelian and superconformal structure, as well as examples of higher rank Mordell-Weil geometries. In addition, in the context of heterotic/F-theory duality, we investigate the role played by multiple K3- and elliptic fibrations in known and novel string dualities in 8-, 6- and 4-dimensional theories. Here we systematically summarize nested fibration structures and comment on the roles they play in T-duality, mirror symmetry, and 4-dimensional compactifications of F-theory with G-flux. This investigation of duality structures is made possible by geometric tools developed in a companion paper [1].

Figures (9)

• Figure 1: An illustration of multiple genus-one fibrations in a single Calabi-Yau $n$-fold: $\pi: X \to B$ and $\pi': X \to B'$
• Figure 2: The abundance of CICY threefold configuration matrices, in the standard list, exhibiting a given number of genus one fibrations which are visible directly in the configuration matrix usscanning.
• Figure 3: The abundance of CICY fourfold configuration matrices, in the standard list, exhibiting a given number of genus one fibrations which are visible directly in the configuration matrix Gray:2014fla.
• Figure 4: Correspondences between different compactifications of M-theory and F-theory associated to geometries with the same total space.
• Figure 5: $6D$ F-theory compactifications that share the same 5D M-theory limit with $n_V^{(5D)}=3, n_H^{(5D)}=48$. The double dashed line denotes a link between two Abelian theories while the thick line denotes a correspondence between non-Abelian and Abelian theories.