2001/02/28 by Tanmay Vachaspati · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.63.105010
published as Phys.Rev. D63 (2001) 105010 · 7 pages; included discussion of gauge fields and other improvements
arxiv created 2001/02/28 · openalex publication_date 2001/04/20 · arxiv updated 2009/11/30 · openalex created_date 2020/07/16 · openalex updated_date 2026/07/28
In a classical, quartic field theory with SU(N)\ifmmode×\else\texttimes\fiZ2 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 \stackrel\ensuremath→N\ensuremath∞, 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(\ensuremathΦ4)]. 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.