Exotic RG Flow of Entanglement Entropy

TL;DR

This paper explores holographic RG flows in a three-dimensional gravity model, classifying their behaviors and analyzing how the entanglement entropy's c-function evolves, confirming its monotonic decrease even with complex beta-functions.

Contribution

It introduces a classification of holographic RG flows based on a parameter in the potential and studies the entanglement entropy's c-function behavior along these flows.

Findings

The entanglement c-function decreases monotonically along RG flows.

Different types of RG flows are classified using potential parameters.

The entanglement entropy results are consistent with holographic renormalization.

Abstract

In this paper, we holographically study the renormalization group (RG) flow in a three-dimensional Einstein-dilaton gravity with a potential permitting several types of the RG flow with nontrivial beta-functions. By using the intrinsic parameter of the potential, we classify possible holographic RG flows and examine their physical features. Using the Ryu-Takayanagi formulation, furthermore, we investigate how the $c$-function of the entanglement entropy behaves along the RG flow numerically. We show that the entanglement $c$-function monotonically decreases even in the cases with a nontrivial beta-function. For checking the consistency, we also compare the result of the entanglement entropy with the $c$-function derived from the holographic renormalization procedure.