2014/10/07 by Murad Alim, Hossein Movasati, Alim, Murad +5
Mathematics · Physics and Astronomy · #14J15 #14N35 #32G20 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #hep-th #math.AG #math.NT #msc:14J15 #msc:14N35 #msc:32G20
paper · pdf · doi:10.48550/arxiv.1410.1889
25 pages
arxiv created 2014/10/07 · arxiv updated 2014/10/09
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 Fgalg, g≥ 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.