A class of Calabi-Yau threefolds as manifolds of SU(2) structure

TL;DR

This paper introduces a class of Calabi-Yau threefolds with SU(2) structure, explores their role in string compactification, and analyzes the resulting supersymmetry breaking and moduli space properties.

Contribution

It constructs abelian fibered Calabi-Yau threefolds with SU(2) structure and studies their impact on supersymmetry breaking and moduli space in string theory.

Findings

SU(2) structure induces N=4 to N=2 supersymmetry breaking

Moduli space analysis matches classical intersection number predictions

Massive modes appear as torsion classes in the cohomology ring

Abstract

A class of abelian fibered Calabi-Yau threefolds X_{m,n} is shown yield SU(2) structure, in addition to the standard SU(3) holonomy. Compactification of type II string theory on a manifold in this class give a 4D effective supergravity theory in which the topology spontaneously breaks N=4 to N=2 supersymmetry. The breaking occurs at a scale hierarchically lower than the compactification scale when the P^1 base is large compared to the T^4 fiber. We analyze the moduli space of SU(2) structure metrics of the N=4 theory and its restriction to the moduli space of Calabi-Yau metrics of the N=2 theory, showing that the latter agrees with the expectation computed from triple intersection numbers in the classical limit. Finally, we analyze the twisted cohomology ring associated with the SU(2) structure of X_{m,n} and show that the breaking of N=4 to N=2 is conveniently summarized in the lifting cohomology classes as one passes to the standard cohomology ring, with massive modes persisting as torsion classes when the coupling is nonminimal. The analysis is facilitated by the existence of explicit first-order metrics obtained by classical supergravity dualities.