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arXiv · 2102.07377

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

Shai M. Chester
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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 $\ell=O(\sqrt{N})$.

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Shai M. Chester. 2021-02-15. Anomalous dimensions of monopole operators in scalar QED$_3$ with Chern-Simons term. https://doi.org/10.1007/jhep07(2021)034

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