2012/06/18 by Michael Schulz, Schulz, Michael B.
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.1206.4027
openalex publication_date 2012/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A class of abelian fibered Calabi-Yau threefolds Xm,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 P1 base is large compared to the T4 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 Xm,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.