Topology and strong four fermion interactions in four dimensions

TL;DR

This paper investigates a four-dimensional massless fermion system with a specific four-fermion interaction, revealing a novel topological structure that enables fermion mass generation without symmetry breaking and proposing a phase transition mechanism.

Contribution

It introduces a new topological structure in the effective action of four-fermion interactions, showing how fermions acquire mass through topological defects without symmetry breaking.

Findings

Fermions gain mass in topologically non-trivial backgrounds.

Defects exhibit logarithmic interactions.

A phase transition separates massless and massive phases.

Abstract

We study massless fermions interacting through a particular four fermion term in four dimensions. Exact symmetries prevent the generation of bilinear fermion mass terms. We determine the structure of the low energy effective action for the auxiliary field needed to generate the four fermion term and find it has an novel structure that admits topologically non-trivial defects with non-zero Hopf invariant. We show that fermions propagating in such a background pick up a mass without breaking symmetries. Furthermore pairs of such defects experience a logarithmic interaction. We argue that a phase transition separates a phase where these defects proliferate from a broken phase where they are bound tightly. We conjecture that by tuning one additional operator the broken phase can be eliminated with a single BKT-like phase transition separating the massless from massive phases.