Coupled fermion-kink system in Jackiw-Rebbi model

Abstract

In this paper we study Jackiw-Rebbi model, in which a massless fermion is coupled to the kink of $\lambda {\varphi }^4$ theory through a Yukawa interaction. In the original Jackiw-Rebbi model the soliton is prescribed. However, we are interested in the back-reaction of the fermion on the soliton besides the effect of the soliton on the fermion. Also, as a particular example, we consider a minimal supersymmetric kink model, $\mathcal{N}=1$, in ($1+1$) dimensions. In this case, the bosonic self-coupling, $\lambda$, and the Yukawa coupling between fermion and soliton, $g$, have specific relation, $g=\sqrt{\lambda /2}$. As the set of coupled equations of motion of the system is not analytically solvable, we use a numerical method to solve it self-consistently. We obtain the bound energy spectrum, bound states of the system and the corresponding shape of the soliton using a relaxation method, except for the zero mode fermionic state and threshold energies which are analytically solvable. With the aid of these results we are able to show how the soliton is affected in general and supersymmetric cases. The results we obtain are consistent with the ones in the literature, considering the soliton as background.

14 pages, 9 figures

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• Kink-antikink collision in the supersymmetric ${\varphi }^4$ model
• Fermion bound states in geometrically deformed backgrounds
• A ${\varphi }^6$ soliton with a long-range tail
• Scattering of fermionic isodoublets on the sine-Gordon kink
• Fermions on wobbling kinks: normal versus quasinormal modes
• Majorana zero mode-soliton duality and in-gap and BIC bound states in modified Toda model coupled to fermion
• Bound States and Particle Production by Breather-Type Background Field Configurations
• Creation of Bound Half-Fermion Pairs by Solitons