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

Abstract

Abstract We study monopole operators at the infrared fixed points of U(1) Chern-Simons-matter theories (QED3, scalar QED3, N=1 $$ \mathcal{N}=1 $$ SQED3, and N=2 $$ \mathcal{N}=2 $$ 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 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 QED3 at κ = 0, we provide conformal bootstrap evidence that this near-degeneracy is in fact maintained to small values of N. For N=2 $$ \mathcal{N}=2 $$ SQED3, we find that the lowest dimension monopole operator is generically non-BPS.

Keywords

• Conformal Field Theory
• Solitons Monopoles and Instantons