The gauge coupling unification in the flipped $E_8$ GUT

Abstract

The gauge coupling unification is investigated at the classical level under the assumptions that the gauge symmetry breaking chain is $E_8\to E_7\times U_1\to E_6\times U_1\to S{O}_{10}\times U_1\to S{U}_5\times U_1\to S{U}_3\times S{U}_2\times U_1$ and only components of the representations 248 of $E_8$ can acquire vacuum expectation values. We demonstrate that there are several options for the relations between the gauge couplings of the resulting theory, but the only symmetry breaking pattern corresponds to ${\alpha }_3={\alpha }_2$ and ${\sin }^2{\theta }_W=3/8$. Moreover, only for this option the particle content of the resulting theory includes all MSSM superfields. It is also noted that this symmetry breaking pattern corresponds to the case when all representation which acquire vacuum expectation values have the minimal absolute values of the relevant $U_1$ charges.

Comments: 45 pages, 1 figure, 6 tables, the version accepted for publication in Theoretical and Mathematical Physics