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Open topological string partition function on compact Calabi-Yau threefoldssatisfies the extended holomorphic anomaly equation. By direct integration, wesolve these equations and obtain partition functions for first several genusand boundaries on complete intersection Calabi-Yau threefolds. Complemented bythe unoriented worldsheet contribution, the annulus functions encode the genusone BPS invariants.

Open Topological String Amplitudes and BPS Invariants on Complete Intersection Calabi-Yau Threefolds