Heterotic SO(32) model building in four dimensions

TL;DR

This paper systematically classifies four-dimensional heterotic SO(32) orbifold models, revealing patterns in twisted spectra and constructing an SO(10) GUT model with four generations, with implications for string dualities.

Contribution

It provides a comprehensive classification of heterotic SO(32) orbifold models based on vectorial gauge shifts, including a parametric determination of twisted spectra and a new SO(10) GUT model.

Findings

All Z3, Z7, Z2N models with vectorial gauge shifts are classified.

Twisted spectra follow a pattern involving vectors and tensors of U(n) and SO(2n) groups.

An SO(10) GUT model with four generations is constructed from the Z4 orbifold.

Abstract

Four dimensional heterotic SO(32) orbifold models are classified systematically with model building applications in mind. We obtain all Z3, Z7 and Z2N models based on vectorial gauge shifts. The resulting gauge groups are reminiscent of those of type-I model building, as they always take the form SO(2n_0)xU(n_1)x...xU(n_{N-1})xSO(2n_N). The complete twisted spectrum is determined simultaneously for all orbifold models in a parametric way depending on n_0,...,n_N, rather than on a model by model basis. This reveals interesting patterns in the twisted states: They are always built out of vectors and anti--symmetric tensors of the U(n) groups, and either vectors or spinors of the SO(2n) groups. Our results may shed additional light on the S-duality between heterotic and type-I strings in four dimensions. As a spin-off we obtain an SO(10) GUT model with four generations from the Z4 orbifold.