A class of kinks in SU(N)× Z₂

الأصل · EN

In a classical, quartic field theory with SU(N) × Z₂ 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→ ∞, 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(Φ⁴)). 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 H/I where H is the unbroken symmetry group and I is the symmetry group that leaves the kink solution invariant.