Calabi-Yau Manifolds and SU(3) Structure

TL;DR

This paper demonstrates the construction of non-trivial SU(3) structures, including Strominger-Hull systems, on a broad class of Calabi-Yau three-folds, enabling new string compactification models with fluxes.

Contribution

It introduces methods to construct SU(3) structures with fluxes on Calabi-Yau three-folds, extending the landscape of string compactifications beyond Ricci-flat metrics.

Findings

SU(3) structures found on all complete intersection Calabi-Yau manifolds

Presence of non-closed three-form fluxes compatible with source terms

Potential for explicit, analytic Calabi-Yau compactifications with fluxes

Abstract

We show that non-trivial SU(3) structures can be constructed on large classes of Calabi-Yau three-folds. Specifically, we focus on Calabi-Yau three-folds constructed as complete intersections in products of projective spaces, although we expect similar methods to apply to other constructions and also to Calabi-Yau four-folds. Among the wide range of possible SU(3) structures we find Strominger-Hull systems, suitable for heterotic or type II string compactifications, on all complete intersection Calabi-Yau manifolds. These SU(3) structures of Strominger-Hull type have a non-vanishing and non-closed three-form flux which needs to be supported by source terms in the associated Bianchi identity. We discuss the possibility of finding such source terms and present first steps towards their explicit construction. Provided suitable sources exist, our methods lead to Calabi-Yau compactifications of string theory with a non Ricci-flat, physical metric which can be written down explicitly and in analytic form.