论文标题
共形相关因子作为动量空间中的单纯形积分
Conformal correlators as simplex integrals in momentum space
论文作者
论文摘要
我们找到了标量$ n $点功能在动量空间和一般维度中的标量$ n $点功能的一般解决方案。该解决方案是根据$（N-1）$ - 简单在动量空间中的简单范围的。 $ n $运算符插入了单纯形的$ n $顶点，而单纯的两个顶点之间运行的动量是集成变量。积分涉及从集成变量构建的动量空间交叉比率的任意函数，而外部动量仅通过每个顶点的动量保护进入。相关器的交叉比例是单一的功能，表现出一种出色的递归结构，其中$ n $ - 点功能是根据$（n-1）$ - 点功能构建的。为了说明我们的讨论，我们在全息形式的保形场理论中得出了$ n $ point contact Witten图的单纯形式。这可以通过一种递归方法以及基于电路理论的星球转换的方法来实现。交叉比率功能的结果表达式涉及$（n-2）$集成，相对于涉及$ n（n-3）/2 $ Integrations的梅林表示，这是一个改进（当$ n> 4 $）。
We find the general solution of the conformal Ward identities for scalar $n$-point functions in momentum space and in general dimension. The solution is given in terms of integrals over $(n-1)$-simplices in momentum space. The $n$ operators are inserted at the $n$ vertices of the simplex, and the momenta running between any two vertices of the simplex are the integration variables. The integrand involves an arbitrary function of momentum-space cross ratios constructed from the integration variables, while the external momenta enter only via momentum conservation at each vertex. Correlators where the function of cross ratios is a monomial exhibit a remarkable recursive structure where $n$-point functions are built in terms of $(n-1)$-point functions. To illustrate our discussion, we derive the simplex representation of $n$-point contact Witten diagrams in a holographic conformal field theory. This can be achieved through both a recursive method, as well as an approach based on the star-mesh transformation of electrical circuit theory. The resulting expression for the function of cross ratios involves $(n-2)$ integrations, which is an improvement (when $n>4$) relative to the Mellin representation that involves $n(n-3)/2$ integrations.
