Space-time random tensor networks and holographic duality

TL;DR

This paper introduces a space-time random tensor network framework that models holographic duality, capturing key properties like entanglement entropy and operator reconstruction without fixed time slicing.

Contribution

It extends spatial tensor networks to a covariant space-time setting, offering a new microscopic approach to holographic duality that incorporates Lorentzian geometries.

Findings

Reproduces covariant Hubeny-Rangamani-Takayanagi formula for entropies

Demonstrates operator correspondence and local reconstruction

Ensures unitarity in Lorentzian spacetime geometries

Abstract

In this paper we propose a space-time random tensor network approach for understanding holographic duality. Using tensor networks with random link projections, we define boundary theories with interesting holographic properties, such as the Renyi entropies satisfying the covariant Hubeny-Rangamani-Takayanagi formula, and operator correspondence with local reconstruction properties. We also investigate the unitarity of boundary theory in spacetime geometries with Lorenzian signature. Compared with the spatial random tensor networks, the space-time generalization does not require a particular time slicing, and provides a more covariant family of microscopic models that may help us to understand holographic duality.