发表机构
University of California, Santa Barbara; Beijing Institute of Mathematical Sciences and Applications（加州大学圣塔芭芭拉分校; 北京数学科学与应用研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出从经典谱曲线及其运动重构最小弦量子方程的方法，通过预解式的解析条件在每亏格有限重构，证明简单分支点下量子修正唯一性，并应用于纯引力、Ising及高阶模型。
AI 中文摘要
最小弦提供了两种研究量子曲面的途径：通过谱曲线或通过微分方程。我们探讨的问题是，在已知经典曲线及其随背景的运动之后，量子方程能在多大程度上被恢复。我们的出发点是标量微分算子的预解式。我们要求其单边界积分仅在分支点处有极点，且所得微分在无穷远处正则。这些条件在每一亏格给出一个有限的重构程序。当分支点是简单的且其能量值移动时，我们证明只要该程序一致，量子修正就是唯一的。一个特定的弦方程若其迹原函数满足相同的解析条件，则提供一个解。标量构造还导出了具有多个边界的振幅。我们通过纯引力和Ising模型引入该方法，然后探索高阶、对偶和非幺正模型。高阶Airy例子将计算与退化轨迹上的r-自旋理论联系起来，后者需要对逆问题进行单独处理。
英文摘要
Minimal strings offer two ways to study quantum surfaces: through a spectral curve or through a differential equation. We ask how much of the quantum equation can be recovered once the classical curve and its motion with the background are known. Our starting point is the resolvent of a scalar differential operator. We require its one-boundary integral to have poles only at branch points, with the resulting differential regular at infinity. These conditions give a finite reconstruction procedure at each genus. When the branch points are simple and their energy values move, we prove that the quantum corrections are unique whenever the procedure is consistent. A specified string equation provides a solution if its trace primitive satisfies the same analytic conditions. The scalar construction also leads to amplitudes with several boundaries. We introduce the method through pure gravity and Ising, then explore higher-order, dual and nonunitary models. Higher-Airy examples connect the calculation to $r$-spin theory on a degenerate locus that requires a separate treatment of the inverse problem.
Comments35 pages + Appendices
