  Rydberg polaritons provide an example of a rare type of system where
three-body interactions can be as strong or even stronger than two-body
interactions. The three-body interactions can be either dispersive or
dissipative, with both types possibly giving rise to exotic,
strongly-interacting, and topological phases of matter. Despite past
theoretical and experimental studies of the regime with dispersive interaction,
the dissipative regime is still mostly unexplored. Using a renormalization
group technique to solve the three-body Schr\"odinger equation, we show how the
shape and strength of dissipative three-body forces can be universally enhanced
for Rydberg polaritons. We demonstrate how these interactions relate to the
transmission through a single-mode cavity, which can be used as a probe of the
three-body physics in current experiments.
