# Interplay between the holographic QCD phase diagram and mutual & $n$-partite information

## TL;DR

This paper explores how mutual and n-partite information behave in holographic QCD phases, revealing complex structures and phase transitions that are consistent with thermodynamic properties, especially below the deconfinement temperature.

## Contribution

It extends previous holographic entanglement studies to include mutual and n-partite information, uncovering rich phase structures and their relation to QCD thermodynamics.

## Key findings

- Rich phase diagram with multiple structures
- Mutual and n-partite information reflect thermodynamic transitions
- No temperature or chemical potential dependence below deconfinement

## Abstract

In earlier work, we studied holographic entanglement entropy in QCD phases using a dynamical Einstein-Maxwell-dilaton gravity model whose dual boundary theory mimics essential features of QCD above and below deconfinement. The model although displays subtle differences compared to the standard QCD phases, however, it introduces a notion of temperature in the phase below the deconfinement critical temperature and captures quite well the entanglement and thermodynamic properties of QCD phases. Here we extend our analysis to study the mutual and $n$-partite information by considering $n$ strips with equal lengths and equal separations, and investigate how these quantities leave their imprints in holographic QCD phases. We discover a rich phase diagram with $n\geq2$ strips and the corresponding mutual and $n$-partite information shows rich structure, consistent with the thermodynamical transitions, while again revealing some subtleties. Below the deconfinement critical temperature, we find no dependence of the mutual and $n$-partite information on temperature and chemical potential.