Experiments in cavity QED defy us to understand how quantum light may affect correlated states of matter, like the paradigmatic fractional quantum Hall effect. In this talk I dive into our recent effort to tackle this very question by studying a simplified light-matter model: the nu=1/3 Laughlin state on a cylinder coupled to a single-cavity mode. Through a mix of analytics and tensor network simulations, we explore ground state and low-energy spectrum properties in the bulk, finding that electric field gradients can give rise to a hybrid light-matter excitation, the 'graviton-polariton' mode.