Gauss-Manin connection in disguise: Calabi-Yau threefolds
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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.1889
- arXiv:
- arXiv:1410.1889
- Bibcode:
- 2014arXiv1410.1889A
- Keywords:
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- Mathematics - Algebraic Geometry;
- High Energy Physics - Theory;
- Mathematics - Number Theory;
- 14N35;
- 14J15;
- 32G20
- E-Print:
- 25 pages