The complex side of the TS/ST correspondence

Understand

The TS/ST correspondence relates the spectral theory of certain quantum mechanical operators, to topological strings on toric Calabi-Yau threefolds.

• So far the correspondence has been formulated for real values of Planck's constant.
• In this paper we start to explore the validity of the correspondence when $\hbar$ takes complex values.
• We give evidence that, for threefolds associated to supersymmetric gauge theories, one can extend the correspondence and obtain exact quantization conditions for the operators.