Feynman diagrams and the large charge expansion in 3 − ε dimensions

In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge n operator in the U(1) model at the Wilson-Fisher fixed point in D=4−ε can be computed semiclassically for arbitrary values of λn, where λ is the perturbatively small fixed point coupling. Here we generalize this result to the fixed point of the U(1) model in 3−ε dimensions. The result interpolates continuously between diagrammatic calculations and the universal conformal superfluid regime for CFTs at large charge. In particular it reproduces the expectedly universal O(n0) contribution to the scaling dimension of large charge operators in 3D CFTs.