Charges of Monopole Operators in \(\widehat{ADE}\) Chern-Simons Quiver Gauge Theories

Abstract

We compute R-charges of the BPS-monopole operators in \(\mathcal{N} = 3\) \(\widehat{ADE}\) Chern-Simons quiver gauge theories, along the lines of the work of Benna, Klebanov and Klose in \cite{bkk}. These theories have a weakly coupled UV completion in terms of \(\mathcal{N}=3\) supersymmetric Chern-Simons Yang-Mills theories. In the UV limit the monopole operators are well approximated by classical solutions. We construct classical BPS and anti-BPS monopole solutions to these theories which preserve \(\frac{1}{3}\) supersymmetry all along the RG flow. We compute the \(SU(2)_R\) charges in these backgrounds and show that the smallest possible value of quantised \(SU(2)_R\) charge is zero in each quiver theory.