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We study monopole operators with the lowest possible topological charge$q=1/2$ at the infrared fixed point of scalar electrodynamics in $2+1$dimension (scalar QED$_3$) with $N$ complex scalars and Chern-Simons coupling$|k|=N$. In the large $N$ expansion, monopole operators in this theory withspins $\ell<O(\sqrt{N})$ and associated flavor representations are expected tohave the same scaling dimension to sub-leading order in $1/N$. We use thestate-operator correspondence to calculate the scaling dimension to sub-leadingorder with the result $N-0.2789+O(1/N)$, which improves on existing leadingorder results. We also compute the $\ell^2/N$ term that breaks the degeneracyto sub-leading order for monopoles with spins $\ell=O(\sqrt{N})$.

Anomalous dimensions of monopole operators in scalar QED$_3$ with Chern-Simons term