Fermion masses through four-fermion condensates

TL;DR

This paper explores a novel mechanism for fermion mass generation via four-fermion condensates, demonstrating a phase transition in a four-dimensional lattice model without symmetry breaking.

Contribution

It extends the study of four-fermion condensate mechanisms to four dimensions, revealing a possible intermediate phase with fermion bilinear condensates.

Findings

Existence of a narrow intermediate phase with fermion bilinear condensates.

Continuous phase transitions separate the phases.

Results are consistent with a second order phase transition in four dimensions.

Abstract

Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the two phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.