Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds

By Yao-Han Chen, Yifan Yang, Noriko Yui, Cord Erdenberger. 2006

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Abstract In this paper we are concerned with the monodromy of Picard-Fuchs differential equations associated with one-parameter families of Calabi-Yau threefolds. Our results show that in the hypergeometric cases the matrix representations of monodromy relative to the Frobenius bases can be expressed in terms of the geometric invariants of the underlying Calabi-Yau threefolds. This phenomenon is also verified numerically for other families of Calabi-Yau threefolds in the paper. Furthermore, we discover that under a suitable change of bases the monodromy groups are contained in certain congruence subgroups of Sp(4, ℤ) of finite index and whose levels are related to the geometric invariants of the Calabi-Yau threefolds.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3873d673f6125a4293e731a57beb68d9589f5394

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions (2006, background): “Φ((2)) should relate Siegel modular forms for admittedly very exotic subgroups [50] of Sp(4,Z) to Calabi-Yau amplitudes.”
New analogues of Clausen’s identities arising from the theory of modular forms | NOVA. The University of Newcastle's Digital Repository (2011, methodology): “3), one can employ the method of [11] to compute the monodromy group approximately and hopefully one can read off the group from the numerical data.”