Entanglement Entropy in a Non-Conformal Background

TL;DR

This paper investigates how entanglement entropy behaves in a non-conformal gauge-gravity duality setting, revealing its dependence on energy scale and temperature, with results showing both increases and decreases relative to conformal cases.

Contribution

It provides a detailed analysis of entanglement entropy in non-conformal backgrounds, highlighting its dependence on energy scale and temperature, and compares it to conformal theories at the UV limit.

Findings

Entanglement entropy decreases with increasing energy scale at zero temperature.

At finite temperature, entanglement entropy increases with the ratio of energy scale to temperature.

The entanglement entropy in non-conformal theories can be larger or smaller than in conformal theories depending on parameters.

Abstract

We use gauge-gravity duality to compute entanglement entropy in a non-conformal background with an energy scale $\Lambda$. At zero temperature, we observe that entanglement entropy decreases by raising $\Lambda$. However, at finite temperature, we realize that both $\frac{\Lambda}{T}$ and entanglement entropy rise together. Comparing entanglement entropy of the non-conformal theory, $S_{A(N)}$, and of its conformal theory at the $UV$ limit, $ S_{A(C)}$, reveals that $S_{A(N)}$ can be larger or smaller than $S_{A(C)}$, depending on the value of $\frac{\Lambda}{T}$.