论文标题
功能方程和变量的分离，以确切的G功能
Functional Equations and Separation of Variables for Exact g-Function
论文作者
论文摘要
G功能是与二维量子场理论边界相关的自由度的度量。在可集成的理论中，可以精确地以弗雷德姆决定因素的形式计算，但是通常很难进行数值评估。在本文中，我们得出了功能方程 - 或同等的热力学伯特·安萨茨（TBA）类型的积分方程 - - - - 直接在最简单的集成理论中直接计算G功能；辛格 - 戈登理论在自偶数点上。该推导基于特雷西（Tracy）的经典结果，以及弗雷德·霍尔姆（Fredholm）决定因素和tba之间的关系，这也用于拓扑字符串。我们通过数值计算来证明我们的配方效率，并将UV限制中的结果与Liouville CFT进行比较。作为一个结果，我们提出了Q-功能的多个积分，我们猜测这些积分来描述G功能的通用部分，并讨论其与可集成的旋转链的影响。
The g-function is a measure of degrees of freedom associated to a boundary of two-dimensional quantum field theories. In integrable theories, it can be computed exactly in a form of the Fredholm determinant, but it is often hard to evaluate numerically. In this paper, we derive functional equations---or equivalently integral equations of the thermodynamic Bethe ansatz (TBA) type---which directly compute the g-function in the simplest integrable theory; the sinh-Gordon theory at the self-dual point. The derivation is based on the classic result by Tracy and Widom on the relation between Fredholm determinants and TBA, which was used also in the context of topological string. We demonstrate the efficiency of our formulation through the numerical computation and compare the results in the UV limit with the Liouville CFT. As a side result, we present multiple integrals of Q-functions which we conjecture to describe a universal part of the g-function, and discuss its implication to integrable spin chains.
