Invariant Tensors in Gauge Theories

TL;DR

This paper introduces a new method for constructing invariant tensors in gauge theories, specifically applied to SO(3) with symmetric tensor fields, aiding in understanding dualities and complex representations.

Contribution

A novel approach to systematically construct all invariant tensors in gauge theories with higher-dimensional field representations.

Findings

Complete set of invariant tensors for SO(3) with symmetric tensor fields identified.

Method simplifies the construction process for complex gauge theory representations.

Enhances understanding of dualities in N=1 gauge theories.

Abstract

Invariant tensors play an important role in gauge theories, for example, in dualities of N=1 gauge theories. However, for theories with fields in representations larger than the fundamental, the full set of invariant tensors is often difficult to construct. We present a new approach to the construction of these tensors, and use it to find the complete set of invariant tensors of a theory of SO(3) with fields in the symmetric tensor representation.