There is an interesting relation between the quantum periods on a certain limit of local ${\mathbb{P}}^1\times {\mathbb{P}}^1$ Calabi-Yau space and a TBA (Thermodynamic Bethe Ansatz) system appeared in the studies of ABJM (Aharony-Bergman-Jafferis-Maldacena) theory. We propose a one-parameter generalization of the relation. Furthermore, we derive the differential operators for quantum periods and the TBA-like equation in various limits of the generalized relation.

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注意量子周期和类似TBA的系统

在一定局限性的量子周期之间存在有趣的关系 ${\mathbb{P}}^{\mathrm{1个}}\times {\mathbb{P}}^{\mathrm{1个}}$在ABJM（Aharony-Bergman-Jafferis-Maldacena）理论的研究中，出现了卡拉比尤空间和一个TBA（热力学Bethe Ansatz）系统。我们提出关系的一参数概括。此外，我们在广义关系的各种限制中导出了量子周期的微分算子和类TBA方程。