BCOV theory on the elliptic curve and higher genus mirror symmetry

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.

56 pages

References in corpus (1)

• Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model

Cited by in corpus (8)

• Vertex algebras and quantum master equation
• On the B-twisted topological sigma model and Calabi-Yau geometry
• Tropical Mirror Symmetry in Dimension One
• Variation of Hodge structures, Frobenius manifolds and Gauge theory
• Renormalization Method and Mirror Symmetry
• Boson-Fermion Correspondence and Holomorphic Anomaly Equation in 2d Yang-Mills Theory on Torus
• Mirror Symmetry for Plane Cubics Revisited
• Algebraic structure of $t{t}^{\ast }$ equations for Calabi-Yau sigma models