Group theory and kink stability equations

Starting from Schrödinger equations withSU(2) group-theoretic potentials, we consider a general family of kinks labeled by two (half-)integers (l, n) with ¦n¦l. A particular choice ofn=0,l=L (L positive integer) leads to a generalL-family, whereL=1 corresponds to sine-Gordon theory, whileL=2 represents the ( ⁴)₁₊₁ model. The ( ⁶)₁₊₁ model can also be recovered withl=3/2,n=–1/2, a particular case of theories labeled byl andn such thatl-n=2 which possess simple kink solutions. We also discuss one-loop order corrections to the kink masses in supersymmetric versions of theL-family. As a byproduct, we obtain the SUSY renormalization of the so-called parameter in sine-Gordon theory.