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arXiv · 1505.05360

New Exact Quantization Condition for Toric Calabi-Yau Geometries

Xin Wang·Guojun Zhang·Min-xin Huang
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Abstract

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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Xin Wang, Guojun Zhang, Min-xin Huang. 2015-05-20. New Exact Quantization Condition for Toric Calabi-Yau Geometries. https://doi.org/10.1103/physrevlett.115.121601

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