Superfloccinaucinihilipilification: Semisimple unifications of any gauge theory

TL;DR

This paper introduces a Mathematica package that systematically finds all anomaly-free, fermion-free semisimple gauge extensions of any given gauge algebra, including grand unified theories and Standard Model extensions.

Contribution

The authors develop a computational tool to classify all semisimple gauge extensions with specific constraints, covering a wide range of theories including GUTs and Standard Model extensions.

Findings

Generated all semisimple completions for Standard Model fermionic extensions.

Provided a comprehensive list of 5835 fermionic Standard Model extensions.

Enabled systematic exploration of anomaly-free gauge theories.

Abstract

We present a Mathematica package that takes any reductive gauge algebra and fully-reducible fermion representation, and outputs all semisimple gauge extensions under the condition that they have no additional fermions, and are free of local anomalies. These include all simple completions, also known as grand unified theories (GUT). We additionally provide a list of all semisimple completions for 5835 fermionic extensions of the one-generation Standard Model.