Fermions on the kink revisited

TL;DR

This paper investigates how localized fermions with backreaction influence the structure of kinks in a 1+1 dimensional ^4 model, revealing significant modifications including oscillations and symmetry violations.

Contribution

It provides a numerical analysis of self-consistent fermion-kink solutions considering backreaction, highlighting the impact on kink profiles and bound states.

Findings

Backreaction causes spatial oscillations in the kink profile.

Fermion backreaction breaks reflection symmetry.

Solutions depend on model parameters.

Abstract

We study fermion modes localized on the kink in the 1+1 dimensional $\phi^4$ model, coupled to the Dirac fermions with backreaction. Using numerical methods we construct self-consistent solutions of the corresponding system of coupled integral-differential equations and study dependencies of the scalar field of the kink and the normalizable fermion bound states on the values of the values of the parameters of the model. We show that the backreaction of the localized fermions significantly modifies the solutions, in particular it results in spatial oscillations of the profile of the kink and violations of the reflection symmetry of the configuration.