# Notes on 8 Majorana Fermions

## TL;DR

This paper explores the triality symmetry of eight Majorana fermions in 1+1 dimensions, highlighting its significance in superstring quantization and topological insulator analysis.

## Contribution

It provides an introduction to the triality of Majorana fermions, emphasizing its role in physical theories and detailed treatment of related symmetries and background structures.

## Key findings

- Demonstrates the triality permuting SO(8) representations
- Connects triality to superstring quantization
- Analyzes symmetries in topological insulators

## 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 ${\bf Z}_2$ global and gauge symmetries and their coupling to background spin structures.