Multiple Fibrations in Calabi-Yau Geometry and String Dualities

TL;DR

This paper investigates Calabi-Yau n-folds with multiple fibrations and their implications for string dualities, revealing how different geometric structures lead to equivalent physical theories across various string frameworks.

Contribution

It provides a systematic analysis of multiple fibrations in Calabi-Yau geometries and their role in dualities like F-theory, M-theory, and heterotic string theories, including new examples and geometric tools.

Findings

Multiple fibrations lead to equivalent M-theory limits from different F-theory vacua.

Identifies new dualities involving higher rank Mordell-Weil geometries.

Systematic classification of nested fibration structures in string compactifications.

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].