$p$-adic Holography from the Hyperbolic Fracton Model

TL;DR

This paper uncovers a duality between a hyperbolic fracton lattice model and multiple copies of Zabrodin's $p$-adic AdS/CFT model, linking subsystem symmetries to $p$-adic geometry and black hole analogs.

Contribution

It establishes a novel low-temperature duality connecting hyperbolic fracton models with $p$-adic holography, highlighting the role of subsystem symmetries and fractal structures.

Findings

Subsystem symmetries act on both boundary and bulk.

Fracton model matches Zabrodin's $p$-adic equations of motion.

Duality extends to $p$-adic black hole analogs.

Abstract

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.