We investigate ten-dimensional gauge theories whose extra six-dimensional space is a compact coset space, $S/R$, and whose gauge group is a direct product of two Lie groups. We list candidates of the gauge group and embeddings of $R$ into them. After dimensional reduction of the coset space, we find fermion and scalar representations of $G_{\mathrm{GUT}}\times \mathrm{U}(1)$ with $G_{\mathrm{GUT}}=\mathrm{SU}(5)$, $\mathrm{SO}(10)$ and $E_6$, which accommodate all of the standard model particles. We also discuss possibilities to generate distinct Yukawa couplings among the generations using representations with different dimensions for $G_{\mathrm{GUT}}=\mathrm{SO}(10)$ and $E_6$ models.

• Received 5 December 2008

DOI:https://doi.org/10.1103/PhysRevD.79.056004