Previous calculations have shown that the 2 particle irreducible (2pi) effective theory is a promising method to study strongly coupled systems, for which non-perturbative techniques are needed. Calculations at the 3 loop level show improved convergence, relative to perturbative results. We present results in \phi^4 theory at the 4 loop level which show that convergence breaks down at large coupling. This indicates the need for higher order effective theories.
4pi calculations in 4 dimensions have never been attempted, because no method is known to deal with the overlapping sub-divergences that appear in these theories. We present a new technique to renormalize the 4pi effective theory, based on a renormalization group approach.