Extended holomorphic anomaly and loop amplitudes in open topological string. (English) Zbl 1194.81219
Summary: 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.
MSC:
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 81T18 | Feynman diagrams |
Keywords:
Calabi-Yau threefolds; Bershadsky, Cecotti, Ooguri and Vafa equation; tadpole cancellation: D-branesReferences:
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