Cavity quantum electrodynamics (QED) manipulates the coupling of light with matter, and allows several emitters to couple coherently with one light mode1. However, even in a many-body system, the light–matter coupling mechanism has so far been restricted to one-body processes. Leveraging cavity QED for the quantum simulation of complex, many-body systems has thus far relied on multi-photon processes, scaling down the light–matter interaction to the low energy and slow time scales of the many-body problem. Here we report cavity QED experiments using molecular transitions in a strongly interacting Fermi gas, directly coupling cavity photons to pairs of atoms. The interplay of strong light–matter and strong interparticle interactions leads to well-resolved pair polaritons—hybrid excitations coherently mixing photons, atom pairs and molecules. The dependence of the pair-polariton spectrum on interatomic interactions is universal, independent of the transition used, demonstrating a direct mapping between pair correlations in the ground state and the optical spectrum. This represents a magnification of many-body effects by two orders of magnitude in energy. In the dispersive regime, it enables fast, minimally destructive measurements of pair correlations, and opens the way to their measurement at the quantum limit and their coherent manipulation using dynamical, quantized optical fields.