BPS relations from spectral problems and blowup equations

2016/09/30 by Alba Grassi, Jie Gu
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Complex system #Duality (order theory) #Geometry and complex manifolds #Integrable system #Invariant (physics) #Quantization (signal processing) #String (physics) #String theory #hep-th #math-ph #math.MP

paper · pdf · doi:10.1007/s11005-019-01163-1

published as Lett. Math. Phys. 109, 1271-1302 (2019) · 26 pages, 3 figures, 2 tables, a few typos corrected

openalex created_date 2016/11/30 · openalex publication_date 2019/02/20 · arxiv created 2021/04/25 · arxiv updated 2021/04/27 · openalex updated_date 2026/08/06

Abstract

Recently an exact duality between topological string and the spectral theory of operators constructed from mirror curves to toric Calabi-Yau threefolds has been proposed. At the same time an exact quantization condition for the cluster integrable systems associated to these geometries has been conjectured. The consistency between the two approaches leads to an infinite set of constraints for the refined BPS invariants of the toric Calabi-Yau threefolds. We prove these constraints for the Y^N,m geometries using the K-theoretic blowup equations for SU(N) SYM with generic Chern-Simons invariant m.

Citations

• Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
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• Quantum geometry of refined topological strings
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