On gauge transformation property of coordinate independent SO(9) vector states in SU(2) Matrix Theory

TL;DR

This paper analyzes coordinate independent SO(9) vector states in SU(2) Matrix theory, identifying their SU(2) representations and showing how certain states relate to the supersymmetric wavefunction expansion.

Contribution

It determines the SU(2) representation decomposition of SO(9) vector states and links a unique adjoint set to the supersymmetric zero energy wavefunction expansion.

Findings

Identified the SU(2) representations of 36 SO(9) vector states.

Found a unique set of states transforming in the adjoint representation.

Linked these states to the linear term in the wavefunction expansion.

Abstract

We investigate coordinate independent SO(9) vector states in SU(2) Matrix theory. There are 36 vector states, and we determine what representations of SU(2) they are decomposed into. Among them we find a unique set of states transforming in adjoint representation. We show that this set of states can appear as the linear term in the coordinate matrices in Taylor expansion of zero energy bound state wavefunction around the origin i.e. it satisfies the condition of full supersymmetry.