Fibrations in Non-simply Connected Calabi-Yau Quotients

TL;DR

This paper investigates genus one fibrations in non-simply connected Calabi-Yau three-folds derived from quotients of CICYs, revealing a high prevalence of multiple fibrations with potential applications in F-theory.

Contribution

It systematically analyzes how discrete symmetries in CICY quotients influence the inheritance of genus one fibrations, expanding understanding of non-simply connected Calabi-Yau manifolds.

Findings

Found 17,161 fibrations on quotient manifolds

Most manifolds exhibit multiple distinct fibrations

Fibrations often have singular bases and multiple fibers

Abstract

In this work we study genus one fibrations in Calabi-Yau three-folds with a non-trivial first fundamental group. The manifolds under consideration are constructed as smooth quotients of complete intersection Calabi-Yau three-folds (CICYs) by a freely acting, discrete automorphism. By probing the compatibility of symmetries with genus one fibrations (that is, discrete group actions which preserve a local decomposition of the manifold into fiber and base) we find fibrations that are inherited from fibrations on the covering spaces. Of the 7,890 CICY three-folds, 195 exhibit known discrete symmetries, leading to a total of 1,695 quotient manifolds. By scanning over 20,700 fiber/symmetry pairs on the covering spaces we find 17,161 fibrations on the quotient Calabi-Yau manifolds. It is found that the vast majority of the non-simply connected manifolds studied exhibit multiple different genus one fibrations - echoing a similar ubiquity of such structures that has been observed in other data sets. The results are available at http://www1.phys.vt.edu/quotientdata/. The possible base manifolds are all singular and are catalogued. These Calabi-Yau fibrations generically exhibit multiple fibers and are of interest in F-theory as backgrounds leading to theories with superconformal loci and discretely charged matter.