Fermion masses without symmetry breaking in two spacetime dimensions

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.

36 pages, no figures. v2: minor changes. v3: added a subsection on parity doubling, replaced appendix B with a review of the Lehmann-Kallen decomposition, revised appendix A, made other minor changes throughout

References in corpus (8)

• Classification of topological insulators and superconductors in three spatial dimensions
• Symmetry Protected Topological phases of Quantum Matter
• Coupling a QFT to a TQFT and Duality
• Interacting fermionic topological insulators/superconductors in three dimensions
• Exotic Quantum Phase Transitions of $(2+1)d$ Dirac fermions
• Interacting Topological Insulator and Emergent Grand Unified Theory
• Parity Doubling Among the Baryons
• Topological number and Fermion Green's function of Strongly Interacting Topological Superconductors

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• Origin of fermion masses without spontaneous symmetry breaking
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• Topological ground state degeneracy of the two-channel Kondo lattice
• Fate of surface gaps in magnetic topological insulators
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