Notes on 8 Majorana Fermions

Abstract

Eight Majorana fermions in $d=1+1$ dimensions enjoy a triality that permutes the representation of the $SO(8)$ global symmetry in which the fermions transform. This triality plays an important role in the quantization of the superstring, and in the analysis of interacting topological insulators and the associated phenomenon of symmetric mass generation. The purpose of these notes is to provide an introduction to the triality and its applications, with careful attention paid to various ${\mathbf{Z}}_2$ global and gauge symmetries and their coupling to background spin structures.

arXiv comment19 pages plus 2 appendices. v2: Typos fixed

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Cited by in corpus (7)

• Symmetric Mass Generation
• Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
• Decorated ${\mathbb{Z}}_2$ Symmetry Defects and Their Time-Reversal Anomalies
• Gapped Chiral Fermions
• Lattice T-duality from non-invertible symmetries in quantum spin chains
• Fermionic Non-Invertible Symmetries in (1+1)d: Gapped and Gapless Phases, Transitions, and Symmetry TFTs
• Boundary RG Flows for Fermions and the Mod 2 Anomaly