Bulk-deformed potentials for toric Fano surfaces, wall-crossing and period

Abstract

We provide an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing techniques and a tropical-holomorphic correspondence theorem for holomorphic discs. As an application of the correspondence theorem, we also prove a big quantum period theorem for toric Fano surfaces which relates the log descendant Gromov-Witten invariants with the oscillatory integrals of the bulk-deformed potentials.

arXiv comment44 pages, 9 figures, comments are welcome

References in corpus (7)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Cyclic symmetry and adic convergence in LagrangianFloer theory
• Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model
• Semi-infinite Hodge structures and mirror symmetry for projective spaces
• Primitive forms via polyvector fields
• Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds
• String topology with gravitational descendants, and periods of Landau-Ginzburg potentials

Cited by in corpus (1)

• Reconstruction of $T_{{\mathbb{P}}^2}$ via tropical Lagrangian multi-section