  We use a post-Gaussian variational approach to non-perturbatively study a
general class of interacting bosonic quantum field theories with generalized
dipole symmetries and fractonic behaviour. We find that while a Gaussian
approach allows to carry out a consistent renormalization group (RG) flow
analysis of these theories, this only grasps the interaction terms associated
to the longitudinal motion of dipoles, which is consistent with previous
analysis using large $N$ techniques. Remarkably, our post-Gaussian proposal, by
providing a variational improved effective potential, is able to capture the
transverse part of the interaction between dipoles in such a way that a non
trivial RG flow for this term is obtained and analyzed. Our results suggest
that dipole symmetries that manifest due to the strong coupling of dipoles, may
robustly emerge at low energies from short distance models without that
symmetry.
