From Path Integrals to Tensor Networks for AdS/CFT

TL;DR

This paper explores tensor network models of AdS/CFT by connecting Euclidean path integrals and quantum state flows, proposing a correspondence with continuous MERA and discussing bulk locality at sub-AdS scales.

Contribution

It introduces a novel approach linking path-integral optimization and quantum state flow to tensor network descriptions of AdS/CFT, supporting a continuous MERA correspondence.

Findings

Path-integral optimization yields states resembling AdS slices.

Flow of quantum states aligns with hyperbolic slices in AdS3.

Heuristic argument suggests sub-AdS bulk locality in holographic CFTs.

Abstract

In this paper, we discuss tensor network descriptions of AdS/CFT from two different viewpoints. First, we start with an Euclidean path-integral computation of ground state wave functions with a UV cut off. We consider its efficient optimization by making its UV cut off position dependent and define a quantum state at each length scale. We conjecture that this path-integral corresponds to a time slice of AdS. Next, we derive a flow of quantum states by rewriting the action of Killing vectors of AdS3 in terms of the dual 2d CFT. Both approaches support a correspondence between the hyperbolic time slice H2 in AdS3 and a version of continuous MERA (cMERA). We also give a heuristic argument why we can expect a sub-AdS scale bulk locality for holographic CFTs.