Monopole Operators in $U(1)$ Chern-Simons-Matter Theories

Abstract

We study 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 $\kappa =k/N$ fixed. In this limit, we extract information about the low-lying spectrum of monopole operators from evaluating the $S^2\times S^1$ partition function in the sector where the $S^2$ is threaded by magnetic flux $4\pi q$. 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 $\kappa =0$, 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 find that the lowest dimension monopole operator is generically non-BPS.

52 pages plus appendices, 9 figures, v2: minor corrections