p-adic CFT is a holographic tensor network

The p-adic AdS/CFT correspondence relates a CFT living on the p-adic numbers to a system living on the Bruhat-Tits tree. Modifying our earlier proposal [1] for a tensor network realization of p-adic AdS/CFT, we prove that the path integral of a p-adic CFT is equivalent to a tensor network on the Bruhat-Tits tree, in the sense that the tensor network reproduces all correlation functions of the p-adic CFT. Our rules give an explicit tensor network for any p-adic CFT (as axiomatized by Melzer), and can be applied not only to the p-adic plane, but also to compute any correlation functions on higher genus p-adic curves. Finally, we apply them to define and study RG flows in p-adic CFTs, establishing in particular that any IR fixed point is itself a p-adic CFT.

p进数的AdS/CFT对应将生活在p进数上的一个共形场论（CFT）与生活在布鲁哈特 - 蒂茨树（Bruhat - Tits tree）上的一个系统联系起来。修改我们早期在[1]中提出的关于p进数AdS/CFT的张量网络实现的提议，我们证明了一个p进数CFT的路径积分等价于布鲁哈特 - 蒂茨树上的一个张量网络，从张量网络能重现p进数CFT的所有关联函数这个意义上来说。我们的规则为任何p进数CFT（如梅尔泽所公理化的那样）给出了一个明确的张量网络，并且不仅可以应用于p进数平面，还可以用于计算更高亏格的p进数曲线上的任何关联函数。最后，我们应用它们来定义和研究p进数CFT中的重整化群流，特别地确定了任何红外不动点本身就是一个p进数CFT。