Renormalization Group Flow of Dirac Composite Fermions at Half Filling

We compare the effects of gauge field fluctuations between different composite fermion descriptions of the half-filled Landau level: the Halperin-Lee-Read (HLR) theory of non-relativistic composite fermions and the theory of Dirac composite fermions recently proposed by Son. While the Dirac theory is explicitly particle-hole symmetric, the HLR theory contains a fluctuating statistical gauge field which appears to break particle-hole symmetry. To better characterize this distinction, we present a renormalization group study of these theories in the presence of Coulomb interactions, using a controlled expansion both in the number of fermion species and the width of the Coulomb potential. In particular, we pay close attention to the effects in the HLR theory that break particle-hole symmetry. We find that both theories are described by marginal Fermi liquid fixed points and compare their universal features.