Calabi-Yau Genus-One Fibrations and Twisted Dimensional Reductions of F-theory

TL;DR

This paper investigates genus one and elliptic fibrations in Calabi-Yau manifolds, highlighting differences in gauge groups arising from twisted reductions in F-theory compactifications.

Contribution

It introduces examples of genus one fibered manifolds with distinct Hodge numbers and gauge groups, and proposes a physical mechanism for these differences in F-theory reductions.

Findings

Examples of genus one fibered manifolds with different Hodge numbers

Different gauge groups from Jacobian fibrations

A proposed physical mechanism for twisted circle reductions

Abstract

In this brief note we explore the space of genus one and elliptic fibrations within CY manifolds, their organizing principles, and how they relate to the set of all CY manifolds. We provide examples of genus one fibered manifolds that exhibit different Hodge numbers -- and physically lead to different gauge groups - than their Jacobian fibrations. We suggest a physical mechanism for understanding this difference in twisted circle reductions of 6-dimensional compactifications of F-theory.