On the SO(9) structure of supersymmetric Yang-Mills quantum mechanics

TL;DR

This paper explores the SO(9) symmetry structure in ten-dimensional supersymmetric Yang-Mills quantum mechanics, constructing explicit singlet states and analyzing fermionic representations to understand symmetry properties.

Contribution

It explicitly constructs the simplest SO(9) singlet state with non-zero fermion number, providing a foundation for building invariant subspaces in supersymmetric Yang-Mills quantum mechanics.

Findings

Constructed the simplest SO(9) singlet state with twelve fermions.

Analyzed the fermionic structure of higher SO(9) irreducible representations.

Identified the non-conservation of Majorana-Weyl fermions under rotations.

Abstract

In ten space-time dimensions the number of Majorana-Weyl fermions is not conserved, not only during the time evolution, but also by rotations. As a consequence the empty Fock state is not rotationally symmetric. We construct explicitly the simplest singlet state which provides the starting point for building up invariant SO(9) subspaces. The state has non-zero fermion number and is a complicated combination of the 1360 elementary, gauge invariant, gluinoless Fock states with twelve fermions. Fermionic structure of higher irreps of SO(9) is also briefly outlined.