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Fermions on one or fewer Kinks

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arxiv 0709.3668 v1 pith:3SQKT4UA submitted 2007-09-23 hep-th

Yi-Zen Chu , Tanmay Vachaspati This is my paper · ORCID
classification hep-th
keywords boundfermionstatesbackgroundfindkink-antikinkstatethere
verification ladder T0 review T1 audit T2 compute T3 formal
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We find the full spectrum of fermion bound states on a Z_2 kink. In addition to the zero mode, there are int[2 m_f/m_s] bound states, where m_f is the fermion and m_s the scalar mass. We also study fermion modes on the background of a well-separated kink-antikink pair. Using a variational argument, we prove that there is at least one bound state in this background, and that the energy of this bound state goes to zero with increasing kink-antikink separation, 2L, and faster than e^{-a2L} where a = min(m_s, 2 m_f). By numerical evaluation, we find some of the low lying bound states explicitly.

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