Class of kinks in SU(N)XZ₂

In a classical, quartic field theory with SU(N)XZ2 symmetry, a class of kink solutions can be found analytically for one special choice of parameters. We construct these solutions and determine their energies. In the limit N-t, the energy of the kink is equal to that of a kink in a Z2 model with the same mass parameter and quartic coupling [coefficient of Tr(<I'4)]. We prove the stability of the solutions to small perturbations but global stability remains unproven. We then argue that the continuum of choices for the boundary conditions leads to a whole space of kink solutions. The kinks in this space occur in classes that are determined by the chosen boundary conditions. Each class is described by the coset space HI I where H is the unbroken symmetry group and / is the symmetry group that leaves the kink solution invariant.