B-model Categorical Enumerative Invariants and holomorphic anomaly equations

Yefeng Shen; Junwu Tu

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arXiv · 2606.07960

B-model Categorical Enumerative Invariants and holomorphic anomaly equations

Yefeng Shen·Junwu Tu

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Abstract

In this paper, we study the B-model categorical enumerative invariants (CEI) associated with derived categories of coherent sheaves on smooth projective Calabi-Yau $3$-folds. We first prove the analogs of the dilaton, string, and divisor equations of CEI in a general context. Then we use these equations and the Givental quantization formula to prove that the B-model CEI for any miniversal family of smooth projective Calabi-Yau $3$-folds satisfies the holomorphic anomaly equations introduced by Bershadsky-Cecotti-Ooguri-Vafa. This provides strong evidence that CEI may be taken as a rigorous mathematical definition of the B-model topological string partition function.

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BibTeX RIS

Yefeng Shen, Junwu Tu. 2026-06-06. B-model Categorical Enumerative Invariants and holomorphic anomaly equations. https://arxiv.org/abs/2606.07960

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