Seidel elements and potential functions of holomorphic disc counting

Abstract

Let M be a symplectic manifold equipped with a Hamiltonian circle action and let L be an invariant Lagrangian submanifold of M. We study the problem of counting holomorphic disc sections of the trivial M-bundle over a disc with boundary in L through degeneration. We obtain a conjectural relationship between the potential function of L and the Seidel element associated to the circle action. When applied to a Lagrangian torus fibre of a semi-positive toric manifold, this degeneration argument reproduces a conjecture (now a theorem) of Chan-Lau-Leung-Tseng relating certain correction terms appearing in the Seidel elements with the potential function.

38 pages, v2: more details added in the proof of Lemma 3.15

References in corpus (4)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Technical details on Kuranishi structure and virtual fundamental chain
• Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds
• Toric degeneration and non-displaceable Lagrangian tori in $S^2\times S^2$

Cited by in corpus (4)

• Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds
• Tropical counting from asymptotic analysis on Maurer-Cartan equations
• An open quantum Kirwan map
• A perturbative construction of primitive forms from log Landau-Ginzburg mirrors of toric manifolds