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Local Mirror Symmetry for One-Legged Topological Vertex

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arxiv 0910.4320 v2 pith:FGNC2EC5 submitted 2009-10-22 math.AG math-phmath.MP

Jian Zhou This is my paper · ORCID
classification math.AGmath-phmath.MP
keywords localmirrorone-leggedsymmetrytopologicalvertexbouchard-maribrane
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abstract

We prove the Bouchard-Mari\~no Conjecture for the framed one-legged topological vertex by deriving the Eynard-Orantin type recursion relations from the cut-and-join equation satisfied by the relevant triple Hodge integrals. This establishes a version of local mirror symmetry for the local $C^3$ geometry with one $D$-brane.

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  1. Quantum Curves in the Context of Symplectic Duality

    math-ph 2025-04 conditional novelty 6.0 of 10

    Quantum spectral curve operators for arbitrary base points can be derived by applying x-y and symplectic duality transformations to simpler spectral curves.

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