Holographic Geometry of Entanglement Renormalization in Quantum Field Theories

TL;DR

This paper explores the connection between holographic geometry and entanglement renormalization in quantum field theories, proposing a metric definition in MERA that aligns with AdS/CFT principles and calculating it for free theories.

Contribution

It introduces a quantum field theoretical definition of the holographic metric in MERA and computes it explicitly for free scalar and fermion theories, linking entanglement renormalization to holography.

Findings

The emergent metric matches AdS/CFT expectations for free theories.

The proposed metric can be extended to time-dependent backgrounds.

Explicit calculations validate the holographic interpretation of MERA.

Abstract

We study a conjectured connection between the AdS/CFT and a real-space quantum renormalization group scheme, the multi-scale entanglement renormalization ansatz (MERA). By making a close contact with the holographic formula of the entanglement entropy, we propose a general definition of the metric in the MERA in the extra holographic direction, which is formulated purely in terms of quantum field theoretical data. Using the continuum version of the MERA (cMERA), we calculate this emergent holographic metric explicitly for free scalar boson and free fermions theories, and check that the metric so computed has the properties expected from AdS/CFT. We also discuss the cMERA in a time-dependent background induced by quantum quench and estimate its corresponding metric.