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arXiv · 1112.4063

BCOV theory on the elliptic curve and higher genus mirror symmetry

Si Li
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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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Si Li. 2011-12-17. BCOV theory on the elliptic curve and higher genus mirror symmetry. https://arxiv.org/abs/1112.4063

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