论文标题
全息四点功能手册
A handbook of holographic 4-point functions
论文作者
论文摘要
我们对动量空间中标量运算符的树级全息$ 4 $点功能进行了全面讨论。我们表明，每个witten图都可以自己满足保形病房身份，因此是有效的保形相关器。当$β=δd/2 $是半综合的，$δ$的操作员的尺寸和$ d $的时空维度可以以封闭形式评估Witten图，并且我们提供了$ d = 3 $和$δ= 2,3 $的显式配方。这些相关因子需要重新归一化，我们明确执行，并导致新的保形异常和β功能。可以通过重量转移操作员链接不同维度的运算符的相关器，这使得可以从给定的“种子”相关器生成新的相关器。我们在动量空间中提出了重量转移算子的新推导，并发现了与使用相关的几个微妙的细微衍生物：此类操作员将交换图映射到交换和接触图的线性组合，并且在需要重新分配时必须特别注意。
We present a comprehensive discussion of tree-level holographic $4$-point functions of scalar operators in momentum space. We show that each individual Witten diagram satisfies the conformal Ward identities on its own and is thus a valid conformal correlator. When the $β= Δ- d/2$ are half-integral, with $Δ$ the dimensions of the operators and $d$ the spacetime dimension, the Witten diagrams can be evaluated in closed form and we present explicit formulae for the case $d=3$ and $Δ=2,3$. These correlators require renormalization, which we carry out explicitly, and lead to new conformal anomalies and beta functions. Correlators of operators of different dimension may be linked via weight-shifting operators, which allow new correlators to be generated from given `seed' correlators. We present a new derivation of weight-shifting operators in momentum space and uncover several subtleties associated with their use: such operators map exchange diagrams to a linear combination of exchange and contact diagrams, and special care must be taken when renormalization is required.
