Monopole operators from the 4 − ϵ expansion

Three-dimensional quantum electrodynamics with n charged fermions contains monopole operators that have been studied perturbatively at large n . here, we initiate the study of these monopole operators in the 4 − ϵ expansion by generalizing them to codimension-3 defect operators in d = 4−ϵ spacetime dimensions. assuming the infrared dynamics is described by an interacting cft, we define the “conformal weight” of these operators in terms of the free energy density on $$ {s}^2times {mathrm{mathbb{h}}}^{2-upepsilon} $$ in the presence of magnetic flux through the s 2, and calculate this quantity to next-to-leading order in ϵ. extrapolating the conformal weight to ϵ = 1 gives an estimate of the scaling dimension of the monopole operators in d = 3 that does not rely on the 1/n expansion. we also perform the computation of the conformal weight in the large n expansion for any d and find agreement between the large n and the small ϵ expansions in their overlapping regime of validity.