Reducing the rank of the gauge group in orbifold compactifications of the heterotic string

Using the fact that the space group of an orbifold is non-abelian, we can reduce the rank of the four-dimensional gauge group obtained from orbifold compactification of the heterotic string. The embedding of the space group in the gauge degrees of freedom is performed by assigning shifts (Wilson lines) in the E₈ × E₈ lattice to the shifts in the six-dimensional lattice, and E₈ × E₈ Weyl rotations to the spatial discrete rotations. Reducing the rank of the gauge group is phenomenologically interesting for explaining the absence of extra low-energy gauge interactions.