We develop the mathematical theory of the open/closed correspondence, proposed by Mayr in physics as a class of dualities between open strings on Calabi-Yau 3-folds and closed strings on Calabi-Yau 4-folds. Given an open geometry on a toric Calabi-Yau 3-orbifold relative to a framed Aganagic-Vafa outer brane, we construct a closed geometry on a toric Calabi-Yau 4-orbifold and establish the correspondence between the two geometries on the following levels across both the A- and B-sides of mirror symmetry: numerical Gromov-Witten invariants; generating functions of Gromov-Witten invariants; B-model hypergeometric functions and Givental-style mirror theorems; Picard-Fuchs systems and solutions; integral cycles on Hori-Vafa mirrors and periods; mixed Hodge structures.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/5che-9h72 |
| Date | January 2023 |
| Creators | Yu, Song |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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