Narrow Results

An algorithm to systematically and efficiently generate free fermionic heterotic string models was recently introduced.¹ 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, . This is obtained in a Layer 1, Order 6 model for which modular invariance itself dictates a gravitino sector accompany the gauge sector.

Using software under development at Baylor University, we explicitly construct all layer 1 gauge, weakly coupled free fermionic heterotic string models up to order 22 in four large spacetime dimensions. The gauge models consist primarily of gauge content making a systematic construction process efficient. We present an overview of the model building procedure, redundancies in the process, methods used to reduce such redundancies and statistics regarding the occurrence of various combinations of gauge group factors and GUT groups. Statistics for both and models are presented.

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 Kač–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.