Abstract

We derive a general expression for the trace of the energy–momentum tensor \(T \kern0.9pt\overline{\vphantom{T}\kern6.0pt}\kern-6.9pt T \)-deformed field theories using a dynamical change of coordinates. Then we perform a dimensional reduction of the bilinear \(T \kern0.9pt\overline{\vphantom{T}\kern6.0pt}\kern-6.9pt T \) operator and obtain a new \(T \kern0.9pt\overline{\vphantom{T}\kern6.0pt}\kern-6.9pt T \)-like deformation of the quantum mechanics of free nonrelativistic fermions and the interacting Calogero–Sutherland system. The deformation leads to a change in the energy spectrum but does not affect the eigenfunctions. Furthermore, an expression for the deformed classical Lagrangian is obtained. We also study the correspondence between the two-dimensional Yang–Mills theory and the Calogero–Sutherland system in the presence of the deformation.

中文翻译：

---

$$T\overline T$$ 通过降维对 Calogero–Sutherland 模型进行变形

摘要

我们使用动态变化推导出能量动量张量迹\(T \kern0.9pt\overline{\vphantom{T}\kern6.0pt}\kern-6.9pt T \) 变形场论的一般表达式的坐标。然后我们对双线性\(T \kern0.9pt\overline{\vphantom{T}\kern6.0pt}\kern-6.9pt T \)算子进行降维，得到一个新的\(T \kern0.9pt\自由非相对论费米子和相互作用的卡洛杰罗-萨瑟兰系统的量子力学的上划线{\vphantom{T}\kern6.0pt}\kern-6.9pt T \)类变形。变形导致能谱发生变化，但不影响本征函数。此外，还获得了变形经典拉格朗日的表达式。我们还研究了存在变形时二维杨-米尔斯理论与卡洛杰罗-萨瑟兰系统之间的对应关系。