This is a write-up of the lectures given in Young Researchers Integrability School 2017. The main goal is to explain the connection between the ODE/IM correspondence and the classical integrability of strings in AdS. As a warm up, we first discuss the classical three-point function of the Liouville theory. Our starting point is the well-known fact that the classical solutions to the Liouville equation can be constructed by solving a certain Schrödinger-like differential equation. We then convert it into a set of functional equations using the idea akin to the ODE/IM correspondence. The classical three-point functions can be computed directly from these functional equations and the result matches with the classical limit of the celebrated DOZZ formula. We then proceed to discuss the semi-classical three-point function of strings in AdS 2 and show that one can apply a similar idea by making use of the classical integrability of the string sigma model on AdS 2 .<...

中文翻译：

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Liouville理论，AdS 2字符串和三点函数

这是《 2017年青年研究人员可整合性学校》中的演讲的改编。主要目的是解释ODE / IM对应关系与AdS中字符串的经典可整合性之间的联系。作为热身，我们首先讨论Liouville理论的经典三点函数。我们的出发点是众所周知的事实，即可以通过求解某个类似于Schrödinger的微分方程来构造Liouville方程的经典解。然后，使用类似于ODE / IM对应的想法将其转换为一组函数方程。可以直接从这些函数方程计算经典三点函数，并且结果与著名的DOZZ公式的经典极限匹配。