Coupled fermion-kink system in Jackiw-Rebbi model

In this paper we study Jackiw-Rebbi model, in which a massless fermion is coupled to the kink of $\lambda \phi^4$ 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.Comment: 14 pages, 9 figure

Quasinormal modes in kink excitations and kink-antikink interactions: a toy model

We study excitations and collisions of kinks in a scalar field theory where the potential has two minima with $Z_2$ symmetry. The field potential is designed to create a square well potential in the stability equation of the kink excitations. The stability equation is analogous to the Schr\"{o}dinger equation, and therefore we use quantum mechanics techniques to study the system. We modify the square well potential continuously, which allows the excitation to tunnel and consequently turns the normal modes of the kink into quasinormal modes. We study the effect of this transition, leading to energy leak, on isolated kink excitations. Finally, we investigate kink-antikink collisions and the resulting scaling and fractal structure of the resonance windows considering both normal and quasinormal modes and compare the results.Comment: 23 pages, 11 figure

An Investigation of the Casimir Energy for a Fermion Coupled to the Sine-Gordon Soliton with Parity Decomposition

We consider a fermion chirally coupled to a prescribed pseudoscalar field in the form of the soliton of the sine-Gordon model and calculate and investigate the Casimir energy and all of the relevant quantities for each parity channel, separately. We present and use a simple prescription to construct the simultaneous eigenstates of the Hamiltonian and parity in the continua from the scattering states. We also use a prescription we had introduced earlier to calculate unique expressions for the phase shifts and check their consistency with both the weak and strong forms of the Levinson theorem. In the graphs of the total and parity decomposed Casimir energies as a function of the parameters of the pseudoscalar field distinctive deformations appear whenever a fermionic bound state energy level with definite parity crosses the line of zero energy. However, the latter graphs reveal some properties of the system which cannot be seen from the graph of the total Casimir energy. Finally we consider a system consisting of a valence fermion in the ground state and find that the most energetically favorable configuration is the one with a soliton of winding number one, and this conclusion does not hold for each parity, separately.Comment: 13 pages, 8 figure

Fermion zero modes in the vortex background of a Chern-Simons-Higgs theory with a hidden sector

In this paper we study a $2+1$ dimensional system in which fermions are coupled to the self-dual topological vortex in $U(1) \times U(1)$ Chern-Simons theory, where both $U(1)$ gauge symmetries are spontaneously broken. We consider two Abelian Higgs scalars with visible and hidden sectors coupled to a fermionic field through three interaction Lagrangians, where one of them violates the fermion number. Using a fine tuning procedure, we could obtain the number of the fermionic zero modes which is equal to the absolute value of the sum of the vortex numbers in the visible and hidden sectors.Comment: 10 page

A ϕ6\phi^6 soliton with a long-range tail

We propose an analytically solvable sextic potential model with non-trivial soliton solutions connecting the trivial vacua. The model does not respect parity symmetry, and like $\phi^4$ theory has two minima. The soliton solutions and the consequent results are obtained in terms of the Lambert W function, i.e., the inverse function of $f(W) = We^W$. They have power-law asymptotics at one spatial infinity and exponential asymptotics at the other. We compare the solution with the kink of $\phi^4$ theory, which preserves the parity symmetry and has exponential asymptotics at both spatial infinities. Moreover, we study the full spectrum (bound and continuum states) of boson and fermion fields in the presence of the proposed soliton. We consider two types of coupling for the boson-soliton interaction and Yukawa coupling for the fermion-soliton interaction. Most results are derived analytically. This property renders the model a fertile ground for further study, including parity breaking related phenomena and long-range soliton-soliton interactions.Comment: 18 pages, 9 figure