https://doi.org/10.1140/epjc/s10052-017-5044-x
Regular Article - Theoretical Physics
Coupled fermion–kink system in Jackiw–Rebbi model
Departamento de Física, Universidade Federal de Pernambuco, Recife, PE, 52171-900, Brazil
* e-mail: andre.amado@ufpe.br
Received:
13
March
2017
Accepted:
1
July
2017
Published online:
13
July
2017
In this paper, we study Jackiw–Rebbi model, in which a massless fermion is coupled to the kink of 
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 in (
) dimensions. In this case, the bosonic self-coupling, 
, and the Yukawa coupling between fermion and soliton, g, have a specific relation, 
. 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.
© The Author(s), 2017
