A Non-Standard String Embedding of E8

TL;DR

This paper introduces a novel string embedding of E8 using an SU(9) structure in free fermionic heterotic string models, expanding the variety of known embeddings and demonstrating a specific model realization.

Contribution

It presents the first realization of E8 via an SU(9) embedding in free fermionic heterotic string models, differing from the standard SO(16) approach.

Findings

E8 realized via SU(9) embedding in a string model

Model constructed at Layer 1, Order 6 with modular invariance constraints

Demonstrates alternative gauge group embedding in string theory

Abstract

An algorithm to systematically and efficiently generate free fermionic heterotic string models was recently introduced. This algorithm has been adopted by the Free Fermionic Model Construction (FFMC) program at Baylor University. As its first application, the algorithm is being applied to systematically generate the complete set of free fermionic heterotic string models with untwisted left-moving (worldsheet supersymmetric) sectors, up to continually advancing Layer and Order. Statistical analysis of this study will be reported in the near future. However, in a series of separate notes we will be reporting some of the more interesting models that appear along the way. In this, our first such note, we reveal a different string embedding of E8 than is standard. That is, rather than realize E8 via an SO(16) embedding, 248 = 120 + 128, we realize it via an SU(9) embedding, 248 = 80 + 84 + 84-bar. This is obtained in a Layer 1, Order 6 model for which modular invariance itself dictates a gravitino sector accompany the gauge sector.