Quantum periods and spectra in dimer models and Calabi-Yau geometries

Journal of High Energy Physics

Xin Wang¹  Min-xin Huang²  Yuji Sugimoto³ 

[1] Bethe Center for Theoretical Physics, Universität Bonn, D-53115, Bonn, Germany;Max Planck Institute for Mathematics, Vivatsgasse 7, D-53111, Bonn, Germany;Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, 230026, Hefei, Anhui, China;Peng Huanwu Center for Fundamental Theory, 230026, Hefei, Anhui, China;

关键词: Differential and Algebraic Geometry;    Lattice Integrable Models;    Topological Strings;   

DOI  :  10.1007/JHEP09(2020)168

来源: Springer

【 摘 要 】

We study a class of quantum integrable systems derived from dimer graphs and also described by local toric Calabi-Yau geometries with higher genus mirror curves, generalizing some previous works on genus one mirror curves. We compute the spectra of the quantum systems both by standard perturbation method and by Bohr-Sommerfeld method with quantum periods as the phase volumes. In this way, we obtain some exact analytic results for the classical and quantum periods of the Calabi-Yau geometries. We also determine the differential operators of the quantum periods and compute the topological string free energy in Nekrasov-Shatashvili (NS) limit. The results agree with calculations from other methods such as the topological vertex.

【 授权许可】

CC BY