Conformal symmetry of the critical point is usually left unused in the perturbative computations of the epsilon expansion series for the Wilson-Fisher fixed point. Conformal bootstrappers would love to do the exact opposite — to reproduce the epsilon expansion from conformal field theory only, without any input from perturbation theory. Here we will present a modest initial result in this direction — use conformal symmetry to derive the anomalous dimensions of $varphi^n$ at the lowest nontrivial order. The recombination of the conformal multiplets of $varphi$ and $varphi^3$ will play a key role.

CERN and LPT ENS