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New Exact Quantization Condition for Toric Calabi-Yau Geometries · Around

2015

New Exact Quantization Condition for Toric Calabi-Yau Geometries

Wang, Xin, Zhang, Guojun, Huang, Min-xin

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We propose a new exact quantization condition for a class of quantum mechanical systems derived from local toric Calabi-Yau three-folds.

Our proposal includes all contributions to the energy spectrum which are non-perturbative in the Planck constant, and is much simpler than the available quantization condition in the literature.
We check that our proposal is consistent with previous works and implies non-trivial relations among the topological Gopakumar-Vafa invariants of the toric Calabi-Yau geometries.
Together with the recent developments, our proposal opens a new avenue in the long investigations at the interface of geometry, topology and quantum mechanics.

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