SU(5) grand unification on a domain-wall brane from an E₆-invariant action

An SU(5) grand unification scheme for effective 3+1-dimensional fields dynamically localised 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 localisation idea. It requires an E_6 gauge-invariant action, yielding a domain-wall solution that has E_6 broken to differently embedded SO(10) x 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 localised left-handed zero-modes in the 5^* + 10 + 1 + 1 representation of SU(5). The remaining ten fermion components of the 27 are delocalised 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 localisation; the single extra dimension is infinite.