Euclidean and Lorentzian Actions of the Classicalized Holographic Tensor Network

TL;DR

This paper introduces a covariant Lorentzian action for the classicalized holographic tensor network in three dimensions, linking it to gravity and exploring its properties, perturbations, and non-equilibrium aspects.

Contribution

It presents the first covariant Lorentzian action for the cHTN as a reduction of the Einstein-Hilbert action in 3D gravity.

Findings

Properties of the Lorentzian cHTN action in the ground state analyzed

Gravity perturbation from a massive particle derived as an Unruh effect

Holographic spacetime formulated as a non-equilibrium second law

Abstract

In three spacetime dimensions, we propose a generally covariant Lorentzian action of the classicalized holographic tensor network (cHTN) as the holographic reduction of the Einstein-Hilbert action of gravity in the presence of a negative cosmological constant. In this article, first, we investigate the properties of this Lorentzian action in the ground state. Next, based on the Euclidean action of the cHTN, we derive the gravity perturbation induced by a massive particle at rest in the cHTN as the Unruh effect. Finally, we view our holographic formulation of spacetime as a non-equilibrium second law subject to general covariance.