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Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions

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Homological Mirror Symmetry

Part of the book series: Lecture Notes in Physics ((LNP,volume 757))

Abstract

The topological string partition function Z(λ,t,t) =exp(λ2 g-2 Fg(t, t)) is calculated on a compact Calabi–Yau M. The Fg(t, t) fulfil the holomorphic anomaly equations, which imply that ψ=Z transforms as a wave function on the symplectic space H3(M, Z). This defines it everywhere in the moduli space M(M) along with preferred local coordinates. Modular properties of the sections Fg as well as local constraints from the 4d effective action allow us to fix Z to a large extent. Currently with a newly found gap condition at the conifold, regularity at the orbifold and the most naive bounds from Castelnuovo’s theory, we can provide the boundary data, which specify Z, e.g. up to genus 51 for the quintic.

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Authors and Affiliations

  1. Department of Physics, University of Wisconsin, Madison, WI 53706, USA

    M.-x. Huang, A. Klemm & S. Quackenbush

  2. Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA

    A. Klemm

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Huang, Mx., Klemm, A., Quackenbush, S. (2008). Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions. In: Homological Mirror Symmetry. Lecture Notes in Physics, vol 757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68030-7_3

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  • DOI: https://doi.org/10.1007/978-3-540-68030-7_3

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