Classification of Standard-like Heterotic-String Vacua

TL;DR

This paper extends the classification of heterotic-string vacua to standard-like models with broken $SO(10)$ symmetry, enabling the generation of millions of phenomenologically viable models with detailed analysis.

Contribution

It introduces a modified classification method for standard-like heterotic-string vacua, allowing efficient identification of models with three generations and specific symmetry breaking.

Findings

Generated approximately 10 million three-generation models.

Identified conditions on GGSO phases for viable models.

Presented an example model with unique phenomenological features.

Abstract

We extend the free fermionic classification methodology to the class of standard-like heterotic-string vacua, in which the $SO(10)$ GUT symmetry is broken at the string level to $SU(3)\times SU(2)\times U(1)^2$. The space of GGSO free phase configurations in this case is vastly enlarged compared to the corresponding $SO(6)\times SO(4)$ and $SU(5)\times U(1)$ vacua. Extracting substantial numbers of phenomenologically viable models therefore requires a modification of the classification methods. This is achieved by identifying conditions on the GGSO projection coefficients, which are satisfied at the $SO(10)$ level by random phase configurations, and that lead to three generation models with the $SO(10)$ symmetry broken to the $SU(3)\times SU(2)\times U(1)^2$ subgroup. Around each of these fertile $SO(10)$ configurations, we perform a complete classification of standard-like models, by adding the $SO(10)$ symmetry breaking basis vectors, and scanning all the associated GGSO phases. Following this methodology we are able to generate some $10^7$ three generation Standard-like Models. We present the results of the classification and one exemplary model with distinct phenomenological properties, compared to previous SLM constructions.