  We present a rigorous framework for linear response theory in cavity QED
materials. Our approach leverages the collective coupling between light and
matter, drawing parallels with large-N theories in quantum field theory. We
derive closed formulas for various responses of both the cavity and the matter.
Our theory is validated by recovering established results for the Dicke model
and the Quantum Hall Effect. Additionally, we discover novel excitations in
quantum magnets, where the cavity binds magnon pairs into localized states.
