GaussManin connection in disguise: CalabiYau threefolds
Abstract
We describe a Lie Algebra on the moduli space of CalabiYau threefolds enhanced with differential forms and its relation to the BershadskyCecottiOoguriVafa 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 nonholomorphic topological string partition functions. Our approach is based on Grothendieck's algebraic de Rham cohomology and on the algebraic GaussManin connection. In this way, we recover a result of YamaguchiYau and AlimLänge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of CalabiYau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.
 Publication:

arXiv eprints
 Pub Date:
 October 2014
 arXiv:
 arXiv:1410.1889
 Bibcode:
 2014arXiv1410.1889A
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 Mathematics  Number Theory;
 14N35;
 14J15;
 32G20
 EPrint:
 25 pages