量子周期-TBA关系的代数证明
Algebraic Proofs of Quantum Period--TBA Relations
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中文总结 AI 辅助
本文通过代数方法证明了量子镜曲线中量子A-周期与TBA类方程之间的两个猜想关系，利用移位乘积、循环量子环面迹和矩阵行列式，在形式幂级数意义下给出严格证明。
中文摘要 AI 辅助
我们给出了量子镜曲线的量子A-周期与热力学Bethe ansatz（TBA）类方程之间两个猜想关系的代数证明。二次关系由移位乘积展开的常数项得出。对于高次关系，一个循环量子环面迹和一个有限矩阵行列式将周期与非重叠杆的自由能联系起来。其密度方程产生TBA类方程，归一化由杆长固定。两个证明均作为复结构参数的形式幂级数成立，并精确依赖于$q=e^{i\hbar}$。
英文摘要
We give algebraic proofs of two conjectural relations between quantum $A$-periods and thermodynamic Bethe ansatz (TBA)-like equations for quantum mirror curves. The quadratic relation follows from constant terms of shifted product expansions. For higher-degree relations, a cyclic quantum-torus trace and a finite matrix determinant identify the period with the free energy of nonoverlapping rods. Their density equation yields the TBA-like equation, with normalization fixed by the rod length. Both proofs hold as formal power series in the complex structure parameter, with exact dependence on $q=e^{i\hbar}$.
发表机构
- University of Science and Technology of China（中国科学技术大学）
- Peng Huanwu Center for Fundamental Theory（彭桓武基础理论中心）
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