  We introduce a technique relying on the use of auxiliary fields in order to
eliminate explicit field-derivatives that plague the high orders
renormalization group treatment of shift-symmetric, derivative, theories. This
technique simplifies drastically the computation of fluctuations in such
theories. This is illustrated by deriving the two-loop renormalization group
equations and the three-loop anomalous dimension of the $\varphi^4$ derivative
theory in $D=4-\epsilon$, which is also relevant to describe the
crumpled-to-flat transition of polymerized membranes. Some features of this
transition are provided.
