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

TL;DR

This paper analytically constructs and analyzes a class of kink solutions in a classical $SU(N) imes Z_2$ symmetric field theory, exploring their energies, stability, and the space of solutions determined by boundary conditions.

Contribution

It provides explicit analytical solutions for kinks in an $SU(N) imes Z_2$ model and characterizes their stability and the structure of the solution space based on boundary conditions.

Findings

Kink energies match those of $Z_2$ models in the large $N$ limit.

Solutions are proven stable against small perturbations.

A continuum of kink solutions exists, classified by boundary conditions and symmetry cosets.

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 ${\rm Tr}(\Phi^4)$). 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.