arXiv 2005.068732020-05hep-th

动量空间中的共形场论和引力中的anomaly作用：三点和四点函数的分析

Conformal field theory in momentum space and anomaly actions in gravity:The analysis of three- and four-point functions

Claudio Corianò, Matteo Maria Maglio

备注：: 110 pages, 5 Figures. To appear on Physics Reports

摘要：

在简要概述了坐标空间中的共形场论的一般方面之后，在第一部分中，我们回顾了在$d\geq 2$维中的动量空间中的三点和四点函数的共形约束的解，其形式为共形Ward恒等式（CWI）。我们的讨论集中在包含应力-能量张量$(T)$、守恒电流$(J)$和标量算子$(O)$的标量算子的分析上。对于标量四点函数，我们简要地讨论了我们的方法来确定这样的方程的对偶共形解，确定只有由CWI的，和有关的共形Yangian对称性，介绍了我们在以前的工作。在包含$T$张量的关联函数中，在平坦时空中计算，共形异常的特征在于特定形状因子中无质量极点的（非局部）交换，这一特征已经在自由场理论和非微扰理论中通过求解共形约束进行了研究。我们讨论的异常有效作用，并说明推导的CWI的直接从它的路径积分定义和Weyl对称性，这是替代的标准operatorial方法在平坦空间的共形场论。对于两点和三点的功能，我们详细说明了这些类型的耦合器的自由场理论的匹配。在一个循环中，对于通用算子$T$、$J$和特定标度维数的标量，通过适当地选择它们的场内容，CFTs的微扰实现提供了CWI所确定的一般解的最简单表达式。在一个技术附录中，我们提供了详细的重建的$TTO$和$TTT$放大器的方法Bzowski，麦克法登和Skenderis，特别是在二级沃德身份的方法，以建立一个完全匹配的微扰描述。

英文摘要：

After a brief outline of general aspects of conformal field theories in coordinate space, in a first part we review the solution of the conformal constraints of three- and four-point functions in momentum space in dimensions $d\geq 2$, in the form of conformal Ward identities (CWI's). We center our discussion on the analysis of correlators containing stress-energy tensors $(T)$, conserved currents $(J)$, and scalar operators $(O)$. For scalar four-point functions, we briefly discuss our method for determining the dual conformal solutions of such equations, identified only by the CWI's, and related to the conformal Yangian symmetry, introduced by us in previous work. In correlation functions with $T$ tensors, evaluated around a flat spacetime, the conformal anomaly is characterized by the (non-local) exchange of massless poles in specific form factors, a signature that has been investigated both in free field theory and non-perturbatively, by solving the conformal constraints. We discuss the anomaly effective action, and illustrate the derivation of the CWI's directly from its path integral definition and its Weyl symmetry, which is alternative to the standard operatorial approach used in conformal field theories in flat space. For two- and three-point functions, we elaborate on the matching of these types of correlators to free-field theories. Perturbative realizations of CFTs at one-loop provide the simplest expressions of the general solutions identified by the CWI's, for generic operators $T$, $J$, and scalars of specific scaling dimensions, by an appropriate choice of their field content. In a technical appendix we offer details on the reconstruction of the $TTO$ and $TTT$ correlators in the approach of Bzowski, McFadden and Skenderis, and specifically on the secondary Ward identities of the method, in order to establish a complete match with the perturbative description.

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