BCOV theory on the elliptic curve and higher genus mirror symmetry

Details BCOV theory on the elliptic curve and higher genus mirror symmetry BCOV theory on the elliptic curve and higher genus mirror symmetry

2011-12-17

arxiv.org/abs/1112.4063v1

Mathematics

Quantum Algebra

56 pages

Scientific paper

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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