Holographic Entanglement Entropy and Renormalization Group Flow

TL;DR

This paper explores how holographic methods can be used to analyze entanglement entropy during RG flows from UV to IR fixed points, revealing geometric insights into degrees of freedom changes and the role of domain walls.

Contribution

It introduces a geometric framework for understanding entanglement entropy in holographic RG flows, highlighting the domain wall's role and the organization of field theory data.

Findings

The domain wall acts as a UV region for the IR theory.

A new area law is controlled by the domain wall.

The proposed formulae are tested in known RG flow examples.

Abstract

Using holography, we study the entanglement entropy of strongly coupled field theories perturbed by operators that trigger an RG flow from a conformal field theory in the ultraviolet (UV) to a new theory in the infrared (IR). The holographic duals of such flows involve a geometry that has the UV and IR regions separated by a transitional structure in the form of a domain wall. We address the question of how the geometric approach to computing the entanglement entropy organizes the field theory data, exposing key features as the change in degrees of freedom across the flow, how the domain wall acts as a UV region for the IR theory, and a new area law controlled by the domain wall. Using a simple but robust model we uncover this organization, and expect much of it to persist in a wide range of holographic RG flow examples. We test our formulae in two known examples of RG flow in 3+1 and 2+1 dimensions that connect non-trivial fixed points.