Free Quotients of Favorable Calabi-Yau Manifolds

TL;DR

This paper classifies cyclic symmetries of certain Calabi-Yau threefolds with new favorable descriptions, identifying numerous potentially topologically new non-simply connected varieties relevant for string theory compactifications.

Contribution

It provides a classification of cyclic symmetries descending from linear actions on ambient spaces of new favorable Calabi-Yau descriptions, revealing many potentially topologically new varieties.

Findings

129 symmetries/non-simply connected Calabi-Yau threefolds identified

At least 33 are potentially topologically new varieties

Classification based on linear actions in new favorable descriptions

Abstract

Non-simply connected Calabi-Yau threefolds play a central role in the study of string compactifications. Such manifolds are usually described by quotienting a simply connected Calabi-Yau variety by a freely acting discrete symmetry. For the Calabi-Yau threefolds described as complete intersections in products of projective spaces, a classification of such symmetries descending from linear actions on the ambient spaces of the varieties has been given in the literature. However, which symmetries can be described in this manner depends upon the description that is being used to represent the manifold. In recent work new, favorable, descriptions were given of this data set of Calabi-Yau threefolds. In this paper, we perform a classification of cyclic symmetries that descend from linear actions on the ambient spaces of these new favorable descriptions. We present a list of 129 symmetries/non-simply connected Calabi-Yau threefolds. Of these, at least 33, and potentially many more, are topologically new varieties.