Abstract
The stability of the topological kinks of the nonlinear S{sup 2}-sigma model discovered by Alonso Izquierdo et al. is discussed by means of a direct estimation of the spectra of the second-order fluctuation operators around topological kinks. The one-loop mass shifts caused by quantum fluctuations around these kinks are computed using the Cahill-Comtet-Glauber formula. The (lack of) stability of the nontopological kinks is unveiled by application of the Morse index theorem. These kinks are identified as non-BPS states. There are two types of topological kinks coming from the twofold embedding of the sine-Gordon model in the massive nonlinear sigma model. It is shown that sine-Gordon kinks of only one type satisfy first-order equations and are accordingly BPS classical solutions. Finally, the interplay between instability and supersymmetry is explored.
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