Central charges of aperiodic holographic tensor network models

TL;DR

This paper establishes a relationship between bulk geometry and boundary central charge in tensor network models of AdS/CFT, introducing models with tunable fractional central charges and connections to quantum error correction and renormalization group methods.

Contribution

It introduces tensor network models based on regular hyperbolic geometries that precisely relate bulk curvature to boundary central charge, including Majorana dimer-based tensors saturating bounds.

Findings

Models exhibit a range of fractional central charges.

Majorana dimer tensors saturate the bounds in large curvature limit.

The renormalization group description is analogous to strong disorder RG.

Abstract

Central to the AdS/CFT correspondence is a precise relationship between the curvature of an anti-de Sitter (AdS) spacetime and the central charge of the dual conformal field theory (CFT) on its boundary. Our work shows that such a relationship can also be established for tensor network models of AdS/CFT based on regular bulk geometries, leading to an analytical form of the maximal central charges exhibited by the boundary states. We identify a class of tensors based on Majorana dimer states that saturate these bounds in the large curvature limit, while also realizing perfect and block-perfect holographic quantum error correcting codes. Furthermore, the renormalization group description of the resulting model is shown to be analogous to the strong disorder renormalization group, thus giving the first example of an exact quantum error correcting code that gives rise to a well-understood critical system. These systems exhibit a large range of fractional central charges, tunable by the choice of bulk tiling. Our approach thus provides a precise physical interpretation of tensor network models on regular hyperbolic geometries and establishes quantitative connections to a wide range of existing models.