Auxiliary Fields Approach to Shift-Symmetric Theories: the Φ^4 Derivative Theory and the Crumpled-to-flat Transition of Membranes at Two-Loop Order

We introduce a technique relying on the use of auxiliary fields in order to eliminate explicit fieldderivatives 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 phi(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.