Classification of Heterotic Pati-Salam Models

TL;DR

This paper extends the classification of heterotic-string models to those with Pati-Salam symmetry, identifying a significant number of three-generation models free of exotic states through statistical sampling.

Contribution

It introduces a new classification method for heterotic-string vacua with Pati-Salam symmetry and provides algebraic expressions for GSO projections, enabling large-scale spectrum analysis.

Findings

Approximately 10^{15} vacua in the class.

One in every 10^{6} vacua yields a three-generation exophobic model.

The method facilitates systematic spectrum analysis of heterotic-string models.

Abstract

We extend the classification of free fermionic heterotic-string models to vacua in which the SO(10) GUT symmetry is broken at the string level to the Pati-Salam subgroup. Using our classification method we recently presented the first example of a quasi--realistic heterotic-string vacuum that is free of massless exotic states. Within this method we are able to derive algebraic expressions for the generalised GSO projections for all sectors that appear in the models. This facilitates the programming of the entire spectrum analysis in a computer code. The total number of vacua in the class of models that we classify is 2^{51} ~ 10^{15}. We perform a statistical sampling in this space of models and extract 10^{11} distinct configurations with Pati-Salam gauge group. Our results demonstrate that one in every 10^{6} vacua correspond to a three generation exophobic model with the required Higgs states, needed to induce spontaneous breaking to the Standard Model.