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

Abstract

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 with spins $\ell <O(\sqrt{N})$ and associated flavor representations are expected to have the same scaling dimension to sub-leading order in $1/N$. We use the state-operator correspondence to calculate the scaling dimension to sub-leading order with the result $N-0.2789+O(1/N)$, which improves on existing leading order results. We also compute the ${\ell }^2/N$ term that breaks the degeneracy to sub-leading order for monopoles with spins $\ell =O(\sqrt{N})$.

21 pages plus appendices, no figures, v3 minor typos fixed

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