Monopole operators in U(1) Chern-Simons-matter theories
We report on monopole operators at the infrared fixed points of U(1) Chern-Simons-matter theories (QED 3 , scalar QED 3 , $\mathcal{N}$=1 SQED 3 , and $\mathcal{N}$=2 SQED 3 ) 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 S 2 × S 1 partition function in the sector where the S 2 is 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 QED 3 at κ = 0, we provide conformal bootstrap evidence that this near-degeneracy is in fact maintained to small values of N . For $\mathcal{N}$=2 SQED 3 , we discover that the lowest dimension monopole operator is generically non-BPS.