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

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.