Fermion masses without symmetry breaking in two spacetime dimensions

TL;DR

This work analyzes whether symmetry-protected fermions can acquire mass without breaking the protecting symmetry in 1+1 dimensions by studying the SO(8) Gross–Neveu model and its SO(7) Kitaev–Fidkowski deformation on the m = 0 manifold. It uses bosonization and triality to relate representations, introduces an emergent Z2' gauge structure, and shows that the KF interaction yields a parity-doubling propagator with a single-particle pole at p^2 = -m_{ ext{kink}}^2$ while forbidding a bare mass term in the numerator. The results imply a doubled Hilbert space along the m = 0 line and a nondegenerate, symmetry-protected ground state, with a concrete link to two- and one-channel Kondo impurity problems that realize the same SO(7) symmetry structure. These findings offer guidance on mass generation in interacting fermion systems and suggest broader implications for higher-dimensional SPT phases and topological superconductors.

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.