Monopole operators in U(1) Chern-Simons-matter theories

We study monopole operators at the infrared fixed points of U(1) Chern-Simons-matter theories (QED₃, scalar QED₃, N= 1 SQED₃, and N= 2 SQED₃) with N matter flavors and Chern-Simons level k. We work in the limit where both N and k are taken to be large with κ = k/N fixed. In this limit, we extract information about the low-lying spectrum of monopole operators from evaluating the S²× S¹partition function in the sector where the S²is threaded by magnetic flux 4πq. At leading order in N, we find a large number of monopole operators with equal scaling dimensions and a wide range of spins and flavor symmetry irreducible representations. In two simple cases, we deduce how the degeneracy in the scaling dimensions is broken by the 1/N corrections. For QED₃at κ = 0, we provide conformal bootstrap evidence that this near-degeneracy is in fact maintained to small values of N. For N= 2 SQED₃, we find that the lowest dimension monopole operator is generically non-BPS.