Emergent bulk gauge field in random tensor networks

TL;DR

This paper introduces a generalized random tensor network model that incorporates bulk gauge fields, linking boundary symmetries to bulk gauge theories and providing insights into holographic duality.

Contribution

It extends random tensor networks to include global symmetries, deriving a quantum extremal surface formula with bulk gauge theory corrections, modeling boundary-bulk symmetry correspondence.

Findings

Renyi entropy described by quantum extremal surface formula

Bulk gauge theory influences entanglement entropy corrections

Boundary symmetry relates to bulk gauge phases

Abstract

Random tensor network states are toy models for holographic duality, which have entanglement properties determined by graph geometry. In this paper, we propose a generalization of the random tensor network states which describe an ensemble of states preserving a given global symmetry. We show that Renyi entropy for this family of states can be described by a quantum extremal surface formula, with corrections to the area law term determined by a bulk gauge theory wavefunction. This provides a toy model of the correspondence between boundary global symmetry and bulk gauge symmetry in holographic duality. We discuss the boundary physical consequences of the bulk deconfined and confined phases.