Communications in Number Theory and Physics

Volume 3 (2009)

Number 1

Evidence for tadpole cancelation in the topological string

Pages: 111 – 172



Johannes Walcher (Institute for Advanced Study, Princeton, New Jersey, U.S.A.)


We study the topological string on compact Calabi–Yau threefolds in the presence of orientifolds and D-branes. In examples, we find that the total topological string amplitude admits a Bogomol’nyi- Prasad-Sommerfield (BPS) expansion only if the topological charge of the D-brane configuration is equal to that of the orientifold plane. We interpret this as a manifestation of a general tadpole cancellation condition in the topological string that is necessary for decoupling A- and B-model in loop amplitudes. Our calculations in the A-model involve an adapted version of existing localization techniques, and give predictions for the real enumerative geometry of higher genus curves in Calabi–Yau manifolds. In the B-model, we introduce an extension of the holomorphic anomaly equation to unoriented strings.

Published 1 January 2009