Aspects of monopole operators in N=6 Chern-Simons theory

TL;DR

This paper studies monopole operators in the $\mathcal{N}=6$ $U(N)\times U(N)$ Chern-Simons-matter theory (ABJM-like) and develops a $1/k$ perturbation theory around exact classical monopole backgrounds to access the spectrum in sectors with flux. By placing the theory on $S^2\times\mathbb{R}$ and solving the classical equations of motion with magnetic flux, the authors construct explicit backgrounds and then quantize fluctuations to leading order in $1/k$, enabling computation of the superconformal index. The resulting index, including monopole sectors, matches the localization results obtained by Kim 2009, with the crucial role played by mixing between gauge fields and certain matter scalars described by odd-dimensional self-duality-like equations. The work also outlines generalizations to more complicated flux patterns and discusses open problems, including the $H\neq\tilde{H}$ sector and implications for open-string dynamics in AdS4/CFT3 contexts.

Abstract

We study local operators of U(N)xU(N) N=6 Chern-Simons-matter theory including a class of magnetic monopole operators. To take into account the interaction of monopoles and basic fields for large Chern-Simons level k, we consider the appropriate perturbation theory in 1/k which reliably describes small excitations around protected chiral operators. We also compute the superconformal index with some simple monopole operators and show that it agrees with the recent result obtained from localization. For this agreement, it is crucial that excitations of gauge fields and some matter scalars mix, which is described classically by odd dimensional self-duality like equations.