Renormalizable 1/N_f Expansion for Field Theories in Extra Dimensions

Understand

We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional field theories.

• It is based on $1/N_f$-expansion and results in a logarithmically divergent perturbation theory in arbitrary high space-time dimension.
• First, we consider a simple example of $N$-component scalar filed theory and then extend this approach to Abelian and non-Abelian gauge theories with $N_f$ fermions.
• In the latter case, due to self-interaction of non-Abelian fields the proposed recipe requires some modification which, however, does not change the main results.