BPS relations from spectral problems and blowup equations.

Recently, an exact duality between topological string and the spectral theory of operators constructed from mirror curves to toric Calabi–Yau threefold has been proposed. At the same time, an exact quantization condition for the cluster integrable systems associated with 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 threefold. 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. [ABSTRACT FROM AUTHOR]