A Fully Solvable Model of Fermionic Interaction in $3+1d$

TL;DR

This paper introduces a fully renormalizable large-N fermionic interaction model in 3+1 dimensions, demonstrating that certain poles in the coupling do not influence physical observables and revealing a phase transition between different stability phases.

Contribution

It extends the understanding of pole effects in quantum field theories by constructing a solvable fermionic model in 3+1d with a phase transition, showing poles do not impact observables.

Findings

Poles in the running coupling do not affect physical observables.

The model exhibits a first-order phase transition.

The theory is fully renormalizable at large-N.

Abstract

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.