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

TL;DR

This paper calculates the sub-leading order scaling dimensions of monopole operators in scalar QED$_3$ with a Chern-Simons term, improving previous leading order results and analyzing degeneracy breaking for higher spins.

Contribution

It provides the first sub-leading order calculation of monopole operator dimensions in scalar QED$_3$ with Chern-Simons coupling, including degeneracy breaking analysis.

Findings

Scaling dimension for monopoles with $q=1/2$ is $N-0.2789+O(1/N)$.

Degeneracy breaking term proportional to $rac{ ext{spin}^2}{N}$ computed.

Results improve upon previous leading order estimates.

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