热Polyakov自举
Thermal Polyakov bootstrap
- School of Physics and Shing-Tung Yau Center, Southeast University（东南大学物理学院及施一公中心）
- Laboratoire de Physique de l’École normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室、ENS、PSL大学、CNRS、索邦大学、巴黎西岱大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文推导了热Polyakov自举方程，用于CFT两点函数，结合热OPE与色散关系，得到满足KMS协变性的块表示，并提出了Polyakov矩阵，为三维Ising CFT的数值研究提供了新方法。
AI中文摘要：
我们推导了在$S^1_\beta\times\mathbb R^{d-1}$上的CFT两点函数的热Polyakov自举方程。将热OPE与色散关系及镜像法相结合，得到了满足Kubo-Martin-Schwinger（KMS）协变性的块表示。它们的局域展开在经典双扭曲维度处包含额外的热块。匹配规定的物理OPE需要抵消这些生成的贡献，从而产生热OPE系数的显式线性方程，包括重构所需的任何补偿项。我们为玻色子标量关联函数和从费米子关联函数提取的反周期标量结构制定了方程，并在解析可处理的热CFT中找到了自洽解。系数矩阵（我们称之为Polyakov矩阵）将大自旋展开与KMS一致性联系起来，并在经典双扭曲谱上简化为负单位矩阵。这一结构为三维Ising CFT提供了一种数值方法，该方法将已知的低位真空数据与自洽的大自旋尾部相结合。
英文摘要：
We derive thermal Polyakov bootstrap equations for CFT two-point functions on $S^1_β\times\mathbb R^{d-1}$. Combining the thermal OPE with a dispersion relation and the method of images gives a representation in blocks that satisfy Kubo-Martin-Schwinger (KMS) covariance. Their local expansions contain additional thermal blocks at classical double-twist dimensions. Matching the prescribed physical OPE requires cancellation of these generated contributions, yielding explicit linear equations for thermal OPE coefficients, including any compensating terms required by the reconstruction. We formulate the equations for bosonic scalar correlators and antiperiodic scalar structures extracted from fermion correlators, and find consistent solutions in analytically tractable thermal CFTs. The coefficient matrix, which we call the Polyakov matrix, connects the large-spin expansion to KMS consistency and reduces to minus the identity on the classical double-twist spectrum. This structure suggests a numerical approach to the three-dimensional Ising CFT that combines known low-lying vacuum data with a self-consistent large-spin tail.
