Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String
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.
Cite
@article{arxiv.0705.4098,
title = {Extended Holomorphic Anomaly and Loop Amplitudes in Open Topological String},
author = {Johannes Walcher},
journal= {arXiv preprint arXiv:0705.4098},
year = {2010}
}