An $SU(5)$ grand unification scheme for effective $3+1$-dimensional fields dynamically localized on a domain-wall brane is constructed. This is achieved through the confluence of the clash-of-symmetries mechanism for symmetry breaking through domain-wall formation, and the Dvali-Shifman gauge-boson localization idea. It requires an $E_6$ gauge-invariant action, yielding a domain-wall solution that has $E_6$ broken to differently embedded $SO(10)\otimes U(1)$ subgroups in the two bulk regions on opposite sides of the wall. On the wall itself, the unbroken symmetry is the intersection of the two bulk subgroups, and contains $SU(5)$. A $4+1$-dimensional fermion family in the 27 of $E_6$ gives rise to localized left-handed zero modes in the $5^{*}\oplus 10\oplus 1\oplus 1$ representation of $SU(5)$. The remaining ten fermion components of the 27 are delocalized exotic states, not appearing in the effective $3+1$-dimensional theory on the domain-wall brane. The scheme is compatible with the type-2 Randall-Sundrum mechanism for graviton localization; the single extra dimension is infinite.

• Received 22 October 2007

DOI:https://doi.org/10.1103/PhysRevD.77.085031