Fermion masses without symmetry breaking in two spacetime dimensions

TL;DR

This paper explores how to generate fermion masses without symmetry breaking in 1+1 dimensions, using models like SO(8) Gross-Neveu and SO(7) Kitaev-Fidkowski, revealing phenomena like parity doubling and connections to condensed matter physics.

Contribution

It demonstrates a mechanism for fermion mass generation without symmetry breaking in low dimensions, providing insights relevant for higher-dimensional theories and condensed matter systems.

Findings

Fermion propagator vanishes at zero momentum

Parity doubling phenomenon observed in the models

Connections established between high energy and condensed matter physics

Abstract

I study the prospect of generating mass for symmetry-protected fermions without breaking the symmetry that forbids quadratic mass terms in the Lagrangian. I focus on 1+1 spacetime dimensions in the hope that this can provide guidance for interacting fermions in 3+1 dimensions. I first review the SO(8) Gross-Neveu model and emphasize a subtlety in the triality transformation. Then I focus on the "m = 0" manifold of the SO(7) Kitaev-Fidkowski model. I argue that this theory exhibits a phenomenon similar to "parity doubling" in hadronic physics, and this leads to the conclusion that the fermion propagator vanishes when p = 0. I also briefly explore a connection between this model and the two-channel, single-impurity Kondo effect. This paper may serve as an introduction to topological superconductors for high energy theorists, and perhaps as a taste of elementary particle physics for condensed matter theorists.