论文标题
在动量空间CFT中，将操作员从单纯形表示
Shift operators from the simplex representation in momentum-space CFT
论文作者
论文摘要
我们在动量空间共形场理论中得出标量运算符的一般$ n $点函数的参数积分表示。最近，这被证明是具有$（N-1）$ - 单纯式拓扑的广义Feynman积分，具有动量空间交叉比例的任意功能。在这里，我们显示了该积分的所有图形多项式，可以用单纯形的Laplacian矩阵的第一和第二次未成年人表示。计算相应电网络节点之间的有效电阻，根据Cayley-Menger基质的决定因素和第一未成年人，可以找到反相反的参数化。这些参数揭示了重量转移操作员的新家族，可作为决定因素，它们连接$ n $ point函数在时空维度中的功能不同。此外，所有以前已知的重量转移操作员的作用都显示出来。最后，新的参数表示能够直接建立保形病房身份的有效性，而无需求助于点数。
We derive parametric integral representations for the general $n$-point function of scalar operators in momentum-space conformal field theory. Recently, this was shown to be expressible as a generalised Feynman integral with the topology of an $(n-1)$-simplex, featuring an arbitrary function of momentum-space cross ratios. Here, we show all graph polynomials for this integral can be expressed in terms of the first and second minors of the Laplacian matrix for the simplex. Computing the effective resistance between nodes of the corresponding electrical network, an inverse parametrisation is found in terms of the determinant and first minors of the Cayley-Menger matrix. These parametrisations reveal new families of weight-shifting operators, expressible as determinants, that connect $n$-point functions in spacetime dimensions differing by two. Moreover, the action of all previously known weight-shifting operators preserving the spacetime dimension is manifest. Finally, the new parametric representations enable the validity of the conformal Ward identities to be established directly, without recourse to recursion in the number of points.
