Renormalization group analysis of resonantly interacting anyons

We formulate a field theory for resonantly interacting anyons, that enables us to perform a perturbative calculation near the fermionic limit. We derive renormalization group equations for three-body and four-body couplings at one-loop order. In addition to two fixed points, we find a limit cycle behavior in the four-body coupling, which implies an infinite set of bound states in the four-anyon system.