论文标题
在动量空间中，重力和CFT的保守电流的四点函数：用TTJJ测试非局部作用
Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ
论文作者
论文摘要
我们对$ ttjj $相关器的扰动实现进行了分析，其中有两个应力能量张量和两个保守的电流，并使用自由田间理论实现，从而在量子校正中整合了保形扇区。这允许在平坦空间周围定义完整异常有效作用的精确扰动扩展 - 最多4分函数 - 可以将预测与异常诱导作用的预测进行比较。后者是以非本地Wess-Zumino动作形式的保形异常约束的变异解。讨论了该相关器的张量结构的重新规范化过程和脱位性，对通用的保形场理论有效，从而得出了其异常的痕量病房身份（WIS）。在此应用程序中，我们还说明了一个一般过程，该过程识别了$ ttjj $和任何$ 4 $ - 点功能的最小数量的紧张结构和相应的形式。将直接计算的结果与从非局部异常诱导作用得出的相同4点函数的表达进行了比较。我们表明，从该动作中得出的$ ttjj $的异常部分的预测，以两个不同的共形分解为Riegert和Fradkin-Vilkovisky（FV）选择，与在扰动$ TTJJ $中确定的异常部分不同，在平面空间限制中，与异常部分有所不同。用Riegert选择计算的相关器的异常部分受双极的影响，而使用FV选择计算的相关器则无法满足保护性WIS。我们介绍了在平坦空间周围的度量扰动中，在第二阶诱导动作的膨胀形式，从而再现了扰动结果。
We present an analysis of the perturbative realization of the $TTJJ$ correlator, with two stress energy tensors and two conserved currents, using free field theory realizations, integrating out conformal sectors in the quantum corrections. This allows defining, around flat space, an exact perturbative expansion of the complete anomaly effective action - up to 4-point functions - whose predictions can be compared against those of the anomaly induced action. The latter is a variational solution of the conformal anomaly constraint at $d=4$ in the form of a nonlocal Wess-Zumino action. The renormalization procedure and the degeneracies of the tensor structures of this correlator are discussed, valid for a generic conformal field theory, deriving its anomalous trace Ward identities (WIs). In this application, we also illustrate a general procedure that identifies the minimal number of tensorial structures and corresponding form factors for the $TTJJ$ and any $4$-point function. The result of the direct computation is compared against the expression of the same 4-point function derived from the nonlocal anomaly induced action. We show that the prediction for the anomalous part of the $TTJJ$ derived from such action, evaluated in two different conformal decompositions, the Riegert and Fradkin-Vilkovisky (FV) choices, differ from the anomaly part identified in the perturbative $TTJJ$, in the flat spacetime limit. The anomaly part of the correlator computed with the Riegert choice is affected by double poles, while the one computed with the FV choice does not satisfy the conservation WIs. We present the correct form of the expansion of the anomaly induced action at the second order in the metric perturbations around flat space that reproduces the perturbative result.
