$p$-adic Holography from the Hyperbolic Fracton Model

We reveal a low-temperature duality between the hyperbolic lattice model featuring fractons and infinite decoupled copies of Zabrodin's $p$-adic model of AdS/CFT. The core of the duality is the subsystem symmetries of the hyperbolic fracton model, which always act on both the boundary and the bulk. These subsystem symmetries are associated with fractal trees embedded in the hyperbolic lattice, which have the same geometry as Zabrodin's model. The fracton model, rewritten as electrostatics theory on these trees, matches the equation of motion of Zabrodin's model. The duality extends from the action to lattice defects as $p$-adic black holes.