论文标题
ADS中的共耦合标量$ _6 $中的4点功能
4-point function from conformally coupled scalar in AdS$_6$
论文作者
论文摘要
我们通过在其自相互作用耦合$λ$的订单中采用幂式扩展顺序，在广告$ _ {6} $中探索共耦合标量理论及其经典解决方案。我们研究标量操作员变形与特定5维综合场理论的全息相关函数，其中操作员从经典溶液中共享相同的缩放尺寸$δ= 3 $。对于我们的解决方案，我们选择一种方案，在该方案中，我们沿着经常出现在经典解决方案中的ADS边界方向上删除Momenta的共线性分歧。这清楚地表明，全息相关函数不含共线性分歧。事实证明，该理论提供了$δ= 3 $标量运算符的正确保形2点和3点功能，如先前的文献所预期。这是有道理的，因为2个点和3点函数是由不依赖共形理论细节的全局形式对称性决定的。我们还从此全息模型中获得了4点功能。实际上，事实证明，4点相关函数不是顺式的，因为它不满足特殊的保形病房身份，尽管它确实具有扩张病房的身份和尊重$ so（5）$旋转对称性。但是，在所有外部动量方向上的共线限制中，四点函数是共形函数，这意味着它满足了特殊的保形病房身份。我们检查该理论的全息$ n $ - 点功能，可以通过采用某种类似Feynman的规则来获得。该规则是通过连接$ l $ - 点功能在$ l <n $的情况下连接$ n $ - 点功能的结构。在共同限制中，这些$ n $ point函数在$ d = 5 $ d = 5 $ d = 5 $ euclidean Space in arxiv中介绍的$δ= 3 $ scall operators的共形$ n $ n $ point函数。
We explore conformally coupled scalar theory in AdS$_{6}$ extensively and their classical solutions by employing power expansion order by order in its self-interaction coupling $λ$. We study holographic correlation functions of scalar operator deformations to a certain 5-dimensional conformal field theory where the operators share the same scaling dimension $Δ=3$, from the classical solutions. For our solutions, we choose a scheme where we remove co-linear divergences of momenta along the AdS boundary directions which frequently appear in the classical solutions. This shows clearly that the holographic correlation functions are free from the co-linear divergences. It turns out that this theory provides correct conformal 2- and 3- point functions of the $Δ=3$ scalar operators as expected in previous literature. It makes sense since 2- and 3- point functions are determined by global conformal symmetry not being dependent on the details of the conformal theory. We also get 4-point function from this holographic model. In fact, it turns out that the 4-point correlation function is not conformal because it does not satisfy the special conformal Ward identity although it does dilation Ward identity and respect $SO(5)$ rotation symmetry. However, in the co-linear limit that all the external momenta are in a same direction, the 4-point function is conformal which means that it satisfy the special conformal Ward identity. We inspect holographic $n$-point functions of this theory which can be obtained by employing a certain Feynman-like rule. This rule is a construction of $n$-point function by connecting $l$-point functions each other where $l<n$. In the co-linear limit, these $n$-point functions reproduce the conformal $n$-point functions of $Δ=3$ scalar operators in $d=5$ Euclidean space addressed in arXiv:2001.05379.
