The conformal bootstrap at finite temperature
The conformal bootstrap at finite temperature
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DOI：
10.1007/jhep10(2018)070
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发表时间：
2018-02
影响因子：
5.4
通讯作者：
Luca V. Iliesiu;Murat Koloğlu;R. Mahajan;Eric Perlmutter;D. Simmons-Duffin
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文献类型：
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作者：
Luca V. Iliesiu;Murat Koloğlu;R. Mahajan;Eric Perlmutter;D. Simmons-Duffin
我们提出了一种方法来约束共形场理论（CFT）的数据在有限的温度下使用的方法的启发，共形引导真空相关函数。我们专注于热的一点和两点函数的本地运营商在平面上。热两点函数的KMS条件被转换为交叉方程。通过研究热两点函数的解析性质，我们导出了一个“热反演公式”，其输出是出现在给定OPE中的所有算子的热一点函数的集合。这涉及到确定一个运动制度，这是四点功能的雷奇制度的模拟。我们通过恢复平均场理论中的谱和热单点函数，以及计算临界O（N）模型中1/N阶的所有高自旋流的热单点函数，证明了反演公式的有效性.此外，我们开发了一个系统的微扰理论的热数据在大自旋，低扭曲的频谱的任何CFT。我们解释了如何反演公式和KMS条件可以结合起来，在有限温度下的算法约束CFTs。在整个过程中，我们绘制类比真空四点函数的自举。最后，我们讨论了未来的热共形引导程序的方向，强调应用到各种类型的CFTs，包括那些与全息投影。
We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one-and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a “thermal inversion formula” whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical O (N) model at leading order in 1/N. Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.