Fermion Mass Generation without Symmetry Breaking

TL;DR

This paper explores how fermion masses can be generated without symmetry breaking, through fluctuations, strong dynamics, or scalar field vacuum expectation values, especially in three-dimensional theories with large fermion flavor numbers.

Contribution

It demonstrates that fermion mass can arise without symmetry breaking and analyzes the transition from crossover to second order phase transition in large N limits.

Findings

Fluctuation-induced fermion mass is suppressed by 1/N.

Mass generation can occur via a rapid crossover or a second order phase transition.

Fermion mass can be generated spontaneously without breaking symmetries except scale symmetry.

Abstract

We study the generation of fermion mass in a context where interactions break a discrete chiral symmetry. Then, fermion mass is not protected by a symmetry, no symmetry is broken by the generation of mass, and a vanishing mass no longer enhances a symmetry. We elaborate these scenarios for template fermionic and Yukawa theories in three dimensions where mass can be generated either by fluctuations, strong dynamics, or the vacuum expectation value of a scalar field. We find that fluctuation-induced contributions to fermion mass are parametrically suppressed in the number of fermion flavours $N$. The generation of fermion mass then takes the form of a rapid crossover which turns into a second order quantum phase transition for large $N$, much like in settings with fundamental chiral symmetry. We further discuss theories where fermion mass can be generated spontaneously without breaking any symmetry other than scale symmetry. Implications of our findings are discussed.