# Holographic Entanglement Entropy in the QCD Phase Diagram with a Critical Point

## TL;DR

This paper investigates how holographic entanglement entropy reflects the phase structure of QCD, especially near the critical point, showing qualitative agreement with thermodynamic phase diagrams and analyzing critical behavior.

## Contribution

It demonstrates that holographic entanglement entropy can effectively characterize QCD phase transitions and critical points, extending previous thermodynamic analyses.

## Key findings

- Entanglement entropy mirrors thermodynamic phase transitions.
- Critical exponents near the critical point are computed.
- Qualitative agreement between entanglement and thermodynamic phase diagrams.

## Abstract

We calculate the holographic entanglement entropy for the holographic QCD phase diagram considered in [Knaute, Yaresko, K\"ampfer (2017), arXiv:1702.06731] and explore the resulting qualitative behavior over the temperature-chemical potential plane. In agreement with the thermodynamic result, the phase diagram exhibits the same critical point as the onset of a first-order phase transition curve. We compare the phase diagram of the entanglement entropy to that of the thermodynamic entropy density and find a striking agreement in the vicinity of the critical point. Thus, the holographic entanglement entropy qualifies to characterize different phase structures. The scaling behavior near the critical point is analyzed through the calculation of critical exponents.