# Matrix Model of QCD: Edge Localized Glue Balls and Phase Transitions

## TL;DR

This paper explores a matrix model of pure SU(2) Yang-Mills theory, revealing boundary-induced edge states, their energy properties, and implications for new QCD phases with an incompressible bulk.

## Contribution

It introduces the concept of boundary-induced edge localized glueball states and their energy behavior within a matrix model of QCD.

## Key findings

- Existence of edge localized glueball states with negative energies.
- Edge levels can be lifted to positive energies with a gluon mass.
- Implication of a new QCD phase with an incompressible bulk.

## Abstract

In a matrix model of pure $SU(2)$ Yang-Mills theory, boundaries emerge in the space of $\textrm{Mat}_{3}(\mathbb{R})$ and the Hamiltonian requires boundary conditions. We show the existence of edge localized glueball states which can have negative energies. These edge levels can be lifted to positive energies if the gluons acquire a London-like mass. This suggests a new phase of QCD with an incompressible bulk.