Imaginary-Time Path-Integral in Bulk Space from the Holographic Principle

TL;DR

This paper derives the imaginary-time path-integral for a particle in AdS space using holographic principles, linking bulk space dynamics to boundary conformal field theory via tensor networks.

Contribution

It introduces a novel derivation of the path-integral in AdS space from holographic tensor networks and classicalized spins, connecting bulk and boundary theories.

Findings

Derived the imaginary-time path-integral from holographic principles.

Linked Euclidean action to classicalized spin actions.

Provided a new perspective on AdS/CFT correspondence.

Abstract

In the three-dimensional anti-de Sitter spacetime/two-dimensional conformal field theory correspondence, we derive the imaginary-time path-integral of a non-relativistic particle in the anti-de Sitter bulk space, which is dual to the ground state, from the holographic principle. This derivation is based on (i) the author's previous argument that the holographic principle asserts that the anti-de Sitter bulk space as a holographic tensor network after classicalization has as many stochastic classicalized spin degrees of freedom as there are sites and (ii) the reinterpretation of the Euclidean action of a free particle as the action of classicalized spins.