Open/closed Correspondence and Extended LG/CY Correspondence for Quintic Threefolds

Chiu-Chu Melissa Liu; Konstantin Aleshkin

Open/closed Correspondence and Extended LG/CY Correspondence for Quintic Threefolds

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arxiv 2309.14628 v3 pith:WENXMSKJ submitted 2023-09-26 math.AG hep-th

Konstantin Aleshkin , Chiu-Chu Melissa Liu This is my paper · ORCID

classification math.AGhep-th

keywords quinticcorrespondenceopenclosedextendedglsmcentralcharge

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We show that Walcher's disk potential for the quintic threefold can be represented as a central charge of a specific Gauged Linear Sigma Model which we call the extended quintic GLSM. This representation provides an open/closed correspondence for the quintic threefold since the central charge is a generating function of closed genus-zero GLSM invariants. We also explain how open Landau-Ginzburg/Calabi-Yau correspondence and open mirror symmetry for the quintic are compatible with wall-crossing and mirror symmetry of the extended GLSM, respectively.

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Hodge-theoretic Open/Closed Correspondence
math.AG 2025-07 conditional novelty 7.0 of 10

The relative periods and mixed Hodge structures of an open toric Calabi-Yau 3-orbifold with a brane agree, up to a Tate twist, with the periods and mixed Hodge structures of a closed toric Calabi-Yau 4-orbifold.

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