Invariant Tensors for $SU(3)$ with Adjoints

TL;DR

This paper introduces a method to identify independent invariant tensors in gauge theories, demonstrated on an $SU(3)$ theory with adjoint matter, advancing the understanding of gauge invariants.

Contribution

The paper presents a novel method linking invariant tensors to constant configurations in field space, specifically applied to $SU(3)$ with adjoint matter.

Findings

Identified the independent invariant tensors for $SU(3)$ with adjoint matter.

Established a theorem relating invariant tensors to constant field configurations.

Provided a systematic approach for analyzing gauge invariants in similar theories.

Abstract

We develop a method for finding the independent invariant tensors of a gauge theory. Our method uses a theorem relating invariant tensors and constant configurations in field space. We apply our method to an $SU(3)$ gauge theory with matter in the adjoint representation, and find the independent invariant tensors of this theory.