title: New Exact Quantization Condition for Toric Calabi-Yau Geometries.
abstract: We propose a new exact quantization condition for a class of quantum mechanical systems derived from local toric Calabi-Yau threefolds. Our proposal includes all contributions to the energy spectrum which are nonperturbative 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 nontrivial 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.
authors.affiliation: Interdisciplinary Center for Theoretical Study, School of Physical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Xin
authors.initials: X
authors.lastname: Wang
authors.affiliation: Interdisciplinary Center for Theoretical Study, School of Physical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Guojun
authors.initials: G
authors.lastname: Zhang
authors.affiliation: Interdisciplinary Center for Theoretical Study, School of Physical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Min-Xin
authors.initials: MX
authors.lastname: Huang