Redundancies in Explicitly Constructed Ten Dimensional Heterotic String Models

TL;DR

This paper investigates redundancies in constructing ten-dimensional heterotic string models using a software framework, revealing the necessity of specific basis vector combinations and limitations in model generation methods.

Contribution

It identifies key redundancies and constraints in the explicit construction of heterotic string models, highlighting the importance of basis vector choices over GSO coefficients alone.

Findings

Maximal supersymmetries occur under specific conditions.

Different basis vector sets are needed to generate all models.

Order combinations influence the models that can be constructed.

Abstract

Using Baylor University's C++ software for construction of weakly coupled free fermionic heterotic string models, called the FF Framework, we explicitly construct the level 1 Ka\v{c}-Moody ten dimensional heterotic string models with the aim of understanding the redundancies endemic to this construction method. We show that for models in any even number of large space-time dimensions with a massless left mover and an odd ordered right mover, the maximal number of space-time supersymmetries are present. We show that in order to produce all of the models for a given order, different basis vectors must be built; one cannot vary only the GSO coefficients. We also show that all combinations of two order-2 basis vectors do not produce the same models as all possible single order-4 basis vectors, implying the product of the orders used in a search does not necessarily determine the models built. We also show that to build all of the D=10 level-1 models the inputs must be: sets of single order-6 basis vectors, pairs of basis vectors with orders 3 and 2, or sets of three order-2 basis vectors.