A fully solvable model of fermionic interaction in 3 + 1d

Recently, Romatschke found that the poles in O(N) scalar theories do not affect observables such as temperature and pressure. Romatschke went on to show this result holds for marginal, relevant, and irrelevant operators in 3 + 1d O(N) scalar theories. We continue in this direction by studying large-N fermi-interactions in 3 + 1d. To do so, we produce a model of marginally coupled fermi-interactions which is fully renormalizable at large-N. This theory contains poles in the running coupling, however we argue these poles do not affect any physical observables. Further, our theory contains first order phase transition which separates a stable, meta-stable, and unstable phase.