Quantized mirror curves and resummed WKB

Journal of High Energy Physics

Szabolcs Zakany¹ 

[1] 0000 0001 2322 4988, grid.8591.5, Département de Physique Théorique, Université de Genève, CH-1211, Genève, Switzerland;

关键词: Topological Strings;    Lattice Integrable Models;    Nonperturbative Effects;   

DOI  :  10.1007/JHEP05(2019)114

来源: publisher

【 摘 要 】

Based on previous insights, we present an ansatz to obtain quantization conditions and eigenfunctions for a family of difference equations which arise from quantized mirror curves in the context of local mirror symmetry of toric Calabi-Yau threefolds. It is a first principles construction, which yields closed expressions for the quantization conditions and the eigenfunctions when ℏ/2π ∈ ℚ, the so-called rational case. The key ingredient is the modular duality structure of the underlying quantum integrable system. We use our ansatz to write down explicit results in some examples, which are successfully checked against purely numerical results for both the spectrum and the eigenfunctions. Concerning the quantization conditions, we also provide evidence that, in the rational case, this method yields a resummation of conjectured quantization conditions involving enumerative invariants of the underlying toric Calabi-Yau threefold.

【 授权许可】

Unknown