Ryu-Takayanagi Formula for Symmetric Random Tensor Networks

TL;DR

This paper extends the Ryu-Takayanagi formula to symmetric random tensor networks with gauge constraints, linking tensor networks to quantum gravity and providing new tools for tensor network/geometry duality.

Contribution

It introduces a novel derivation of the RT formula for symmetric RTNs, connecting tensor networks with group field theories and quantum gravity.

Findings

RT formula recovered in large bond regime

Extension of RTN formalism with gauge symmetry

Links tensor networks to quantum gravity tools

Abstract

We consider the special case of Random Tensor Networks (RTN) endowed with gauge symmetry constraints on each tensor. We compute the R\`enyi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background independent quantum gravity, and for importing quantum gravity tools in tensor network research.