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arXiv · 1410.1889

Gauss-Manin connection in disguise: Calabi-Yau threefolds

Murad Alim·Hossein Movasati·Emanuel Scheidegger·Shing-Tung Yau
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Abstract

We describe a Lie Algebra on the moduli space of Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions $F_g^{alg}, g\geq 1$, which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck's algebraic de Rham cohomology and on the algebraic Gauss-Manin connection. In this way, we recover a result of Yamaguchi-Yau and Alim-Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi-Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.

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Murad Alim, Hossein Movasati, Emanuel Scheidegger, Shing-Tung Yau. 2014-10-07. Gauss-Manin connection in disguise: Calabi-Yau threefolds. https://arxiv.org/abs/1410.1889

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