E6Tensors: A Mathematica Package for E6 Tensors

TL;DR

E6Tensors is a Mathematica package designed to facilitate explicit tensor calculations in E6 gauge theories, providing tools for group generators, structure constants, and various tensor representations.

Contribution

It introduces a comprehensive Mathematica package that automates tensor computations and lists gauge-invariant terms for E6 theories, aiding theoretical physics research.

Findings

Provides explicit matrix expressions for E6 generators

Includes structure constants and higher rank tensors

Lists gauge-invariant superpotential and Lagrangian terms

Abstract

We present the Mathematica package E6Tensors, a tool for explicit tensor calculations in E6 gauge theories. In addition to matrix expressions for the group generators of E6, it provides structure constants, various higher rank tensors and expressions for the representations 27, 78, 351 and 351'. This paper comes along with a short manual including physically relevant examples. I further give a complete list of gauge invariant, renormalisable terms for superpotentials and Lagrangians.