Conformal Quasicrystals and Holography

TL;DR

This paper introduces conformal quasicrystals as a new discrete geometric structure for modeling boundary degrees of freedom in holographic tensor networks, enabling conformal field theory discretizations that preserve key symmetries.

Contribution

It presents the construction of conformal quasicrystals, including higher-dimensional examples, as a novel approach to discretizing conformal geometry in holography.

Findings

Boundary degrees of freedom live on conformal quasicrystals

Constructed 1D and higher-dimensional conformal quasicrystals

Discretizations preserve an infinite subgroup of the conformal group

Abstract

Recent studies of holographic tensor network models defined on regular tessellations of hyperbolic space have not yet addressed the underlying discrete geometry of the boundary. We show that the boundary degrees of freedom naturally live on a novel structure, a conformal quasicrystal, that provides a discrete model of conformal geometry. We introduce and construct a class of one-dimensional conformal quasicrystals, and discuss a higher-dimensional example (related to the Penrose tiling). Our construction permits discretizations of conformal field theories that preserve an infinite discrete subgroup of the global conformal group at the cost of lattice periodicity.