论文标题
在动量空间和重力中的拓扑术语中的四个点功能
Four point functions in momentum space and topological terms in gravity
论文作者
论文摘要
在第一部分中，我们专注于坐标空间中的CFT。我们奠定了保形场理论的基础，我们还展示了一种方法，其中通过使用嵌入形式主义，我们可以得出N-Point标量形式的保形相关器。我们在动量空间中进行分析，并说明了保形异常的理论。我们继续通过反对者分析相关因素的重新归一化，然后讨论异常作用。在论文的第二部分中。我们得出并分析了动量空间中通用CFT的张力4点功能的共形病房身份（CWI）。相关器涉及应力 - 能量张量$ t $和三个标量算子$ o $（$ tooo $）。我们将相应CWIS的结构得出了两组不同的变量，与1到3（1 graviton $ \ \ $ 3标量）和2至2（graviton + scalar $ \至$两个标量）散射过程有关。 然后，我们转到另一个由四个应力能量张量制成的保形相关器。我们详细介绍了在平坦的时空限制下的重力波动$（h）$的扩展中，在重力波动$（h）$中的扩展中，详细介绍了最高第4次阶的结构。我们讨论了四个时空维度中包含应力能量张量（4T）插入应力能量张量（4T）的4分函数的重归其化。 最后，我们包括对重新归一化涉及的拓扑术语的分析，并因此对重力理论进行了校正。
In the first part, we concentrate on CFTs in coordinate space. We lay the foundations of Conformal Field Theory and we also demonstrate a method where by using the embedding formalism we can derive up to n-point scalar conformal correlators. We proceed with our analysis in momentum space and we illustrate the theory of the conformal anomalies. We move on to analyse the renormalization of the correlators through counterterms followed by a discussion of the anomaly action. In the second part of the thesis. we derive and analyze the conformal Ward identities (CWIs) of a tensorial 4-point function of a generic CFT in momentum space. The correlator involves the stress-energy tensor $T$ and three scalar operators $O$ ($TOOO$). We derive the structure of the corresponding CWIs in two different sets of variables, relevant for the analysis of the 1-to-3 (1 graviton $\to$ 3 scalars) and 2-to-2 (graviton + scalar $\to$ two scalars) scattering processes. Then, we move on to another conformal correlator, the one made of four stress-energy tensors. We elaborate on the structure of the conformal anomaly effective action up to 4-th order, in an expansion in the gravitational fluctuations $(h)$ of the background metric, in the flat spacetime limit. We discuss the renormalization of 4-point functions containing insertions of stress-energy tensors (4T), in conformal field theories in four spacetime dimensions. Finally, we include an analysis on the topological terms that are involved in the renormalization and consequently corrections of gravitational theories.
