Topological Strings and Quantum Spectral Problems

Understand

We consider certain quantum spectral problems appearing in the study of local Calabi-Yau geometries.

• The quantum spectrum can be computed by the Bohr-Sommerfeld quantization condition for a period integral.
• For the case of small Planck constant, the periods are computed perturbatively by deformation of the Omega background parameters in the Nekrasov-Shatashvili limit.
• We compare the calculations with the results from the standard perturbation theory for the quantum Hamiltonian.