B-model CEI on Calabi-Yau 3-folds satisfy holomorphic anomaly equations after proving dilaton/string/divisor analogs and applying Givental quantization.
BCOV theory on the elliptic curve and higher genus mirror symmetry
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abstract
We develop the quantum Kodaira-Spencer theory on the elliptic curve and establish the corresponding higher genus B-model. We show that the partition functions of the higher genus B-model on the elliptic curve are almost holomorphic modular forms, which can be identified with partition functions of descendant Gromov-Witten invariants on the mirror elliptic curve. This gives the first compact Calabi-Yau example where mirror symmetry is established at all genera.
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B-model Categorical Enumerative Invariants and holomorphic anomaly equations
B-model CEI on Calabi-Yau 3-folds satisfy holomorphic anomaly equations after proving dilaton/string/divisor analogs and applying Givental quantization.