Algorithm for determining U(1) charges in free fermionic heterotic string models

TL;DR

This paper introduces an algorithm to determine U(1) gauge charges in free fermionic heterotic string models, aiding the search for realistic string phenomenology by analyzing gauge charges efficiently.

Contribution

It presents a new algorithm for calculating U(1) charges in WCFFHS models, including its computational complexity and implementation details.

Findings

U(1) charges influence matter state uniqueness in models

Preliminary analysis of 1.4 million models shows significant impact of U(1) charges

Algorithm can be integrated with existing string model-building frameworks

Abstract

To assist in the search for phenomenologically realistic models in the string landscape, we must develop tools for investigating all gauge charges, including U(1) charges, in string models. We introduce the process for constructing fermionic string models and present an algorithm for determining the U(1) gauge states and U(1) charges in weakly-coupled free fermionic heterotic string (WCFFHS) models given their matter and non-Abelian gauge content. We determine the computational complexity of this algorithm and discuss a particular implementation that can be used in conjunction with a framework developed at Baylor University for building WCFFHS models. We also present preliminary results regarding matter state uniqueness for a run of 1.4 million gauge models and find that U(1) charges affect the number of unique matter states in a significant minority of models constructed. We conclude by considering future avenues of investigation to which this algorithm may be applied.