Special properties of a submanifold of su(3)

TL;DR

This paper explores a special submanifold of su(3), revealing linear gauge transformations, a new parameterization of SU(3), and geometric insights relating to E8 rotations, enhancing understanding of gauge symmetries.

Contribution

It introduces a linear finite gauge transformation in a specific su(3) submanifold and provides a novel parameterization of SU(3) using a single octet vector.

Findings

Finite gauge transformation is linear in gauge functions.

A parameterization of SU(3) with a single octet vector is achieved.

A geometric interpretation in terms of E8 rotations is presented.

Abstract

The finite gauge transformation, in the submanifold of su(3) introduced in hep-th/9902027, is found to be linear in the gauge functions ${\omega}^a$'s. In this manner, a parameterization of SU(3) in terms of a single real octet vector ${\omega}^a$ is achieved. Under this finite transformation, those gauge fields satisfying $D^{ab}_{\mu}{\omega}^b = 0$, remain unchanged. A geometric meaning to the submanifold in terms of rotations in E8 is presented.