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29 March 2024
 
  » arxiv » 1410.1889

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Gauss-Manin connection in disguise: Calabi-Yau threefolds
Murad Alim ; Hossein Movasati ; Emanuel Scheidegger ; Shing-Tung Yau ;
Date 7 Oct 2014
AbstractWe 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 $F_g^{alg}, ggeq 1$, 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-L"ange 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.
Source arXiv, 1410.1889
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