Holographic Tensor Networks with Bulk Gauge Symmetries

TL;DR

This paper introduces a new class of holographic tensor network models with bulk gauge symmetries, enabling the study of more general entanglement structures beyond fixed-area states.

Contribution

It constructs a gauge-invariant tensor network model that captures nontrivial entanglement features and satisfies the quantum-corrected Ryu-Takayanagi formula.

Findings

Model satisfies quantum-corrected Ryu-Takayanagi formula

Includes a gauge theory on a general graph

Reveals nontrivial R extsuperscript{n} entropy contributions

Abstract

Tensor networks are useful toy models for understanding the structure of entanglement in holographic states and reconstruction of bulk operators within the entanglement wedge. They are, however, constrained to only prepare so-called "fixed-area states" with flat entanglement spectra, limiting their utility in understanding general features of holographic entanglement. Here, we overcome this limitation by constructing a variant of random tensor networks that enjoys bulk gauge symmetries. Our model includes a gauge theory on a general graph, whose gauge-invariant states are fed into a random tensor network. We show that the model satisfies the quantum-corrected Ryu-Takayanagi formula with a nontrivial area operator living in the center of a gauge-invariant algebra. We also demonstrate nontrivial, n-dependent contributions to the R\'enyi entropy and R\'enyi mutual information from this area operator, a feature shared by general holographic states.