A-model Implications of Extended Mirror Symmetry
Lukas Hahn, Johannes Walcher
TL;DR
This paper extends the A-model variation of mixed Hodge structures to incorporate open Gromov-Witten invariants, aligning with extended mirror symmetry predictions for Calabi-Yau threefolds.
Contribution
It introduces a new framework connecting cohomological structures on Lagrangian submanifolds with extended mirror symmetry, incorporating recent axioms for open Gromov-Witten theory.
Findings
Extended A-model Hodge structure matches mirror symmetry predictions.
Connects cohomology ring structures with open Gromov-Witten invariants.
Provides a new perspective on mirror symmetry for Calabi-Yau threefolds.
Abstract
Associativity of the quantum product ensures flatness of the Dubrovin connection and is the basis for Hodge-theoretic mirror symmetry of Calabi-Yau threefolds. We use ring and module structure on cohomology pertaining to a Lagrangian submanifold to define an extension of the A-model Variation of mixed Hodge structure that matches the predictions from extended mirror symmetry. Our construction makes contact with axioms for open Gromov-Witten theory recently proposed by Solomon-Tukachinsky.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry