标题： 杨振宁环恒等式用于鱼网四点积分 显示英文标题

标题： Yangian Ward Identities for Fishnet Four-Point Integrals

摘要： 我们推导并研究了无限类四点阶梯积分及其Basso-Dixon推广的Yangian守恒定律。这些对称性方程来自于将相应的费曼积分解释为双标量鱼网理论中的关联函数。另外，所提出的恒等式可以理解为动量空间共形对称性的异常方程。Ward恒等式表现为定义Appell超几何函数的部分微分方程的非齐次扩展。我们采用显式共形张量约化来以紧凑形式表达这些非齐次项，这些项由具有位移维度和传播子幂的Basso-Dixon积分的线性组合给出。Ward恒等式自然地推广到一个一参数D维积分族，这些积分代表Kazakov和Olivucci广义鱼网理论中的关联函数。当指定到二维时空时，Yangian Ward恒等式解耦。通过变量分离，我们显式地自举了共形2D框积分的解。结果是Yangian不变积的线性组合，这些积在传播子幂的各向同性选择下简化为椭圆K积分。我们评论了二维和四维中超越性模式的差异及其与不连续性的关系。 显示英文摘要

摘要： We derive and study Yangian Ward identities for the infinite class of four-point ladder integrals and their Basso-Dixon generalisations. These symmetry equations follow from interpreting the respective Feynman integrals as correlation functions in the bi-scalar fishnet theory. Alternatively, the presented identities can be understood as anomaly equations for a momentum space conformal symmetry. The Ward identities take the form of inhomogeneous extensions of the partial differential equations defining the Appell hypergeometric functions. We employ a manifestly conformal tensor reduction in order to express these inhomogeneities in compact form, which are given by linear combinations of Basso-Dixon integrals with shifted dimensions and propagator powers. The Ward identities naturally generalise to a one-parameter family of D-dimensional integrals representing correlators in the generalised fishnet theory of Kazakov and Olivucci. When specified to two spacetime dimensions, the Yangian Ward identities decouple. Using separation of variables, we explicitly bootstrap the solution for the conformal 2D box integral. The result is a linear combination of Yangian invariant products of Legendre functions, which reduce to elliptic K integrals for an isotropic choice of propagator powers. We comment on differences in the transcendentality patterns in two and four dimensions and their relations to discontinuities.