Mean-field theory for self-interacting relativistic Luttinger fermions

TL;DR

This paper explores relativistic Luttinger fermion models with self-interactions, classifies mass terms, and uses mean-field theory to identify phase transitions and low-energy behaviors, revealing models with dimensional transmutation and gapped phases.

Contribution

It introduces a classification of mass terms and applies mean-field theory to analyze phase structure in relativistic Luttinger fermion models with large flavor numbers.

Findings

Identification of asymptotically free coupling branches.

Discovery of models undergoing dimensional transmutation.

Analysis of gapped phases and propagator structures.

Abstract

We investigate a class of quantum field theories with relativistic Luttinger fermions and local self-interaction in scalar channels. For an understanding of possible low-energy phases, we first classify the set of mass terms arising from scalar fermion bilinears. For large flavor numbers, we show that each of our models features a coupling branch in which the theory is asymptotically free. In order to address the long-range behavior, we use mean-field theory which is exact in the limit of large flavor numbers. We identify two models which undergo dimensional transmutation, interconnecting the asymptotically free high-energy regime with an ordered low-energy phase sustaining a vacuum condensate. We also study the analytic structure of the Luttinger-fermionic propagator in the various possible gapped phases.