1998/08/20 by Marcos Mariño, Marcos Marino, Gregory Moore · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Biology #Black Holes and Theoretical Physics #Calabi–Yau manifold #Compactification (mathematics) #Fibration #Genus #Geometry and complex manifolds #Heterotic string theory #Holomorphic function #Homotopy #Mathematical physics #Mathematics #Moduli space #Pure mathematics #Riemann surface #hep-th
paper · pdf · doi:10.1016/s0550-3213(98)00847-5
published as Nucl.Phys. B543 (1999) 592-614 · 26 pages, harvmac b mode
arxiv created 1998/08/20 · openalex publication_date 1999/03/01 · arxiv updated 2017/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We explicitly evaluate the low energy coupling Fg in a d = 4, N = 2 compactification of the heterotic string. The holomorphic piece of this expression provides the information not encoded in the holomorphic anomaly equations, and we find that it is given by an elementary polylogarithm with index 3 - 2g, thus generalizing in a natural way the known results for g = 0, 1. The heterotic model has a dual Calabi-Yau compactification of the type 11 string. We compare the answer with the general form expected from curve-counting formulae and find good agreement. As a corollary of this comparison we predict some numbers of higher genus curves in a specific Calabi-Yau, and extract some intersection numbers on the moduli space of genus-g Riemann surfaces.