2005/12/31 by Albrecht Klemm, Marcos Mariño, Marcos Marino · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Anomaly (physics) #Black Holes and Theoretical Physics #Computation #Heterotic string theory #Holomorphic function #Homotopy and Cohomology in Algebraic Topology #Realization (probability) #String (physics) #String theory #Symmetry (geometry) #Topological string theory #Topology (electrical circuits) #hep-th #math.AG
paper · pdf · doi:10.1007/s00220-007-0407-z
published as Commun.Math.Phys.280:27-76,2008 · 62 pages, v3: some results at genus 3 corrected, more typos corrected
arxiv created 2006/12/15 · openalex publication_date 2008/03/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study topological string amplitudes for the FHSV model using various techniques. This model has a type II realization involving a Calabi-Yau threefold with Enriques fibres, which we call the Enriques Calabi-Yau. By applying heterotic/type IIA duality, we compute the topological amplitudes in the fibre to all genera. It turns out that there are two different ways to do the computation that lead to topological couplings with different BPS content. One of them leads to the standard D0-D2 counting amplitudes, and from the other one we obtain information about bound states of D0-D4-D2 branes on the Enriques fibre. We also study the model using mirror symmetry and the holomorphic anomaly equations. We verify in this way the heterotic results for the D0-D2 generating functional for low genera and find closed expressions for the topological amplitudes on the total space in terms of modular forms, and up to genus four. This model turns out to be much simpler than the generic B-model and might be exactly solvable.