A class of kinks in SU(N)\times Z_2

Abstract

In a classical, quartic field theory with $SU(N)\times Z_2$ 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 $N\to \infty$, the energy of the kink is equal to that of a kink in a $Z_2$ model with the same mass parameter and quartic coupling (coefficient of $\mathrm{Tr}({\Phi }^4)$). 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 $H/I$ where $H$ is the unbroken symmetry group and $I$ is the symmetry group that leaves the kink solution invariant.

7 pages; included discussion of gauge fields and other improvements

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