Conformal Quasicrystals and Holography
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.
Keywords
Cite
@article{arxiv.1805.02665,
title = {Conformal Quasicrystals and Holography},
author = {Latham Boyle and Madeline Dickens and Felix Flicker},
journal= {arXiv preprint arXiv:1805.02665},
year = {2020}
}
Comments
v1: 8 pages, 4 figures; v2: 9 pages, 4 figures, expanded Introduction and Discussion, added references, matches version to be published in PRX