Colored HOMFLYPT counts holomorphic curves.
basic_science · Level V
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- Record sourced from PubMed, PMID 41385545.
- Also identified by DOI 10.1073/pnas.2510118122 and PMC identifier 12718330.
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Abstract
Given a link in the three-sphere, its Lagrangian conormal can be transplanted to the "resolved conifold," which is a certain noncompact Calabi-Yau threefold. Here we show that, as predicted by Ooguri and Vafa using string theoretic arguments, the count of all holomorphic curves in the resolved conifold ending on this Lagrangian is, appropriately understood, the collection of the HOMFLYPT invariants of all colorings of the link. This generalizes our previous work, Skeins on branes, arXiv:1901.08027, which identified a curve count that captures the uncolored case. The main ingredient in the present work is a skein-valued multiple cover formula for an isolated embedded annulus.