Anomalous dimensions of monopole operators in scalar QED3 with Chern-Simons term

A bstract 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 ℓ < O 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 . 2743 + O (1/ N ), which improves on existing leading order results. We also compute the ℓ 2 / N term that breaks the degeneracy to sub-leading order for monopoles with spins ℓ = O N .