Abstract
We study a fermion field coupled to a scalar via a Yukawa term. The scalar field is the $\phi^4$ model with an impurity that preserves half of the BPS property. We analyze the spectrum of the defects of the model and collisions between them both close to the BPS regime and not. As the fermion binds to these defects, it may be transferred from one to the other, which we quantify via overlaps, known as Bogoliubov coefficients. BPS collisions are less likely to transfer the fermion between defects and can be adiabatic for non-relativistic velocities, especially for small coupling constants. Moreover, closer to the BPS limit only a small fraction of the fermion number is radiated away. In contrast, non-BPS collisions lead to more radiation in the fermion field and excitation of the fermion to higher bound states, and the result is more sensitive to the parameters.
Highlights
Interactions of the fermion field with solitons have been subject to intense research since the pioneering work of Jackiw and Rebbi [1]
The main goal in this work is to compare the fermion transfer between solitons when these solitons collide in BPS and non-BPS cases
In order to do this, we added a fermion field and a Yukawa interaction to a model recently proposed in the literature [45] that consists of the φ4 model with a half-BPS preserving impurity
Summary
Interactions of the fermion field with solitons have been subject to intense research since the pioneering work of Jackiw and Rebbi [1]. This problem becomes more interesting when one considers a kink-antikink pair, instead of just a kink, as the background This was done in [5] for the φ4 model where the authors computed the energy spectrum and eigenstates of a fermion in such background. They showed that, as the distance of the kink-antikink increases, the fermion bound states and energy approach the ones of a single kink, as expected. Similar half-BPS preserving models with exactly solvable BPS sector were considered in [47] Supersymmetric extensions of these models, where the scalar field naturally couples to a fermion field, were studied in [48].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
