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arXiv · 0705.4098

Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String

Johannes Walcher
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Abstract

Open topological string amplitudes on compact Calabi-Yau threefolds are shown to satisfy an extension of the holomorphic anomaly equation of Bershadsky, Cecotti, Ooguri and Vafa. The total topological charge of the D-brane configuration must vanish in order to satisfy tadpole cancellation. The boundary state of such D-branes is holomorphically captured by a Hodge theoretic normal function. Its Griffiths' infinitesimal invariant is the analogue of the closed string Yukawa coupling and plays the role of the terminator in a Feynman diagram expansion for the topological string with D-branes. The holomorphic anomaly equation is solved and the holomorphic ambiguity is fixed for some representative worldsheets of low genus and with few boundaries on the real quintic.

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Johannes Walcher. 2009-02-04. Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String. https://doi.org/10.1016/j.nuclphysb.2009.02.006

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