Frame ambiguity in Open Gromov-Witten invariants

Abstract

We consider Open Gromov-Witten invariants for noncompact Calabi-Yau in the case the Lagrangian has the topology of ${\mathbb{R}}^2\times S^1$. The definition of the invariant involves the choice of a frame for the Lagrangian, in accord with string theory. Our result applies to the examples arising from Large $N$-duality. In particular it leads to knot and link invariants counting holomorphic curves.

Improved exposition

References in corpus (7)

• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Disk Instantons, Mirror Symmetry and the Duality Web
• Framed knots at large N
• Moduli of J-Holomorphic Curves with Lagrangian Boundary Conditions and Open Gromov-Witten Invariants for an $S^1$-Equivariant Pair
• Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc
• Open Gromov-Witten theory on Calabi-Yau three-folds II
• Conormal bundles, contact homology and knot invariants

Cited by in corpus (5)

• Open topological strings and integrable hierarchies: Remodeling the A-model
• Open Gromov-Witten theory on Calabi-Yau three-folds II
• Open Gromov-Witten theory without Obstruction
• Kontsevich-Soibelman Wall Crossing Formula and Holomorphic Disks
• Open Gromov-Witten invariants and Boundary States