Large N Chern-Simons-matter fixed points with multiple flavors

Abstract

In this paper we analyze the $2+1$d conformal fixed points arising from $SU(N_c)$ Chern-Simons-matter theories with multiple flavors $N_f > 1$ in the 't Hooft large $N_c$ limit. The multi-flavor generalization of quasi-fermionic theories (fermions or critical scalars coupled to Chern-Simons gauge fields) is straightforward, but this is not true for quasi-bosonic theories (scalars or critical fermions coupled to Chern-Simons gauge fields). The latter theories have three flavor-singlet relevant operators and also three marginal operators, that become exactly marginal for infinite $N_c$, but have a non-zero beta function at order $1/N_c$. We compute the beta functions of these couplings in various weak coupling limits, and discuss also their general structure, generalizing previous computations for $N_f=1$. We find that IR-stable fixed points of the marginal couplings exist for some values of $N_f$ and of the 't Hooft coupling $\lambda$, but not for other values, and in one case we can explicitly follow how two pairs of fixed points merge and disappear as $\lambda$ is increased. We also analyze the ``Semi-Critical'' conformal field theories that arise when fine-tuning two (rather than three) relevant operators, and compute the beta function for their (single) marginal coupling constant.