  Light-matter interactions of defects in two dimensional materials are
expected to be profoundly impacted by strong coupling to phonons. In this work,
we combine ab initio calculations of a defect in hBN, with a fully quantum
mechanical and numerically exact description of a cavity-defect system to
elucidate this impact. We show that even at weak light-matter coupling, the
dynamical evolution of the cavity-defect system has clear signatures of
non-markovian phonon effects, and that linear absorption spectra show the
emergence of hybridised light-matter-phonon states in regimes of strong
light-matter coupling. We emphasise that our methodology is general, and can be
applied to a wide variety of material/defect systems.
