  We revisit the order $\varepsilon$ dilatation operator of the Wilson-Fisher
fixed point obtained by Kehrein, Pismak, and Wegner in light of recent results
in conformal field theory. Our approach is algebraic and based only on symmetry
principles. The starting point of our analysis is that the first correction to
the dilatation operator is a conformal invariant, which implies that its form
is fixed up to an infinite set of coefficients associated with the scaling
dimensions of higher-spin currents. These coefficients can be fixed using
well-known perturbative results, however, they were recently re-obtained using
CFT arguments without relying on perturbation theory. Our analysis then implies
that all order-$\varepsilon$ scaling dimensions of the Wilson-Fisher fixed
point can be fixed by symmetry.
