Title: Conformal four-point ladder integrals in diverse dimensions and polylogarithms Show Chinese title

Title: 共形四点梯形积分在不同维数中的多对数

Abstract: In the paper, the family of conformal four-point ladder diagrams in arbitrary space-time dimensions is considered. We use the representation obtained via explicit calculation using the operator approach and conformal quantum mechanics to study their properties, such as symmetries, loop and dimensional shift identities. In even integer dimensions, latter allows one to reduce the problem to two-dimensional case, where the notable factorization holds. Additionally, for a specific choice of propagator powers, we show that the representation can be written in the form of linear combinations of classical polylogarithms (with coefficients that are rational functions) and explore the structure of the resulting expressions. Show Chinese abstract

Abstract: 在论文中，考虑了任意时空维度下的共形四点梯形图族。 我们使用通过使用算子方法和共形量子力学进行显式计算得到的表示来研究它们的性质，如对称性、环路和维度移位恒等式。 在偶数整数维度中，后者允许将问题简化为二维情况，在这种情况下存在显著的分解。 此外，对于传播子幂的特定选择，我们表明该表示可以写成经典多对数的线性组合（系数为有理函数），并探讨了所得表达式的结构。