The making of Calabi-Yau spaces: Beyond toric hypersurfaces

TL;DR

This paper explores the construction of new Calabi-Yau threefolds beyond toric hypersurfaces, emphasizing conifold transitions and the connectivity of moduli spaces, with implications for string theory.

Contribution

It introduces a new class of Calabi-Yau spaces with small Picard numbers and their mirrors, expanding the known landscape beyond toric hypersurfaces.

Findings

Constructed a large class of new CY spaces via conifold transitions

Demonstrated connectivity of moduli spaces through singular transitions

Highlighted potential for broader exploration of Calabi-Yau geometries

Abstract

While Calabi-Yau hypersurfaces in toric ambient spaces provide a huge number of examples, theoretical considerations as well as applications to string phenomenology often suggest a broader perspective. With even the question of finiteness of diffeomorphism types of CY 3-folds unsettled, an important idea is Reid's conjecture that the moduli spaces are connected by certain singular transitions. We summarize the results of our recent construction of a large class of new CY spaces with small Picard numbers and of their mirrors via conifold transitions and discuss the benefits of other approaches to interesting locations in the web that have been or should be pursued.