Free Fermionic Heterotic Model Building and Root Systems

TL;DR

This paper introduces a root system-based approach to derive the GSO Projection in free fermionic heterotic string models, along with an efficient algorithm for generating basis vectors to study model landscape statistics.

Contribution

It provides a novel root system interpretation of the GSO Projection and an optimized algorithm for systematic basis vector generation in heterotic string model building.

Findings

Significant computational efficiency improvement at order 6

Algorithm reduces computational cost in landscape statistics

Applied method to a simple class of models

Abstract

We consider an alternative derivation of the GSO Projection in the free fermionic construction of the weakly coupled heterotic string in terms of root systems, as well as the interpretation of the GSO Projection in this picture. We then present an algorithm to systematically and efficiently generate input sets (i.e. basis vectors) in order to study Landscape statistics with minimal computational cost. For example, the improvement at order 6 is approximately 10^{-13} over a traditional brute force approach, and improvement increases with order. We then consider an example of statistics on a relatively simple class of models.