This review describes a link between Lax operators, embedded surfaces and thermodynamic Bethe ansatz equations for integrable quantum field theories. This surprising connection between classical and quantum models is undoubtedly one of the most striking discoveries that emerged from the off-critical generalisation of the ODE/IM correspondence, which initially involved only conformal invariant quantum field theories. We will mainly focus of the KdV and sinh-Gordon models. However, various aspects of other interesting systems, such as affine Toda field theories and non-linear sigma models, will be mentioned. We also discuss the implications of these ideas in the AdS/CFT context, involving minimal surfaces and Wilson loops. This work is a follow-up of the ODE/IM review published more than ten years ago by J. Phys. A: Math. Theor. , before the discovery of its off-critical generalisation and the corresponding geometrical interpretation.

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ODE / IM对应关系的几何方面

这篇综述描述了Lax算子，嵌入表面和热力学Bethe ansatz方程之间关于可积分量子场理论的联系。经典模型和量子模型之间的这种令人惊讶的联系无疑是最引人注目的发现之一，该发现是由ODE / IM对应关系的非关键性概括得出的，ODE / IM对应关系最初仅涉及共形不变量子场理论。我们将主要关注KdV和sinh-Gordon模型。但是，将提到其他有趣系统的各个方面，例如仿射Toda场论和非线性sigma模型。我们还将在AdS / CFT上下文中讨论这些想法的含义，涉及最小的曲面和Wilson循环。这项工作是十多年前由J. Phys发表的ODE / IM评论的后续工作。答：数学。理论。，