Exact solutions to quantum spectral curves by topological string theory

Understand

We generalize the conjectured connection between quantum spectral problems and topological strings to many local almost del Pezzo surfaces with arbitrary mass parameters.

• The conjecture uses perturbative information of the topological string in the unrefined and the Nekrasov-Shatashvili limit to solve non-perturbatively the quantum spectral problem.
• We consider the quantum spectral curves for the local almost del Pezzo surfaces of $\mathbb{F}_2$, $\mathbb{F}_1$, the blowup of $\mathbb{P}^2$ in two points and a mass deformation of the $E_8$ del Pezzo corresponding to different deformations of the three-term operators $\mathsf{O}_{1,1}$, $\mathsf{O}_{1,2}$ and $\mathsf{O}_{2,3}$.
• To check the conjecture, we compare the predictions for the spectrum of these operators with numerical results for the eigenvalues.