Fermion scattering on topological solitons in the ${\mathbb{CP}}^{N-1}$ model

Abstract

The scattering of Dirac fermions in the background fields of topological solitons of the $(2+1)$-dimensional ${\mathbb{CP}}^{N-1}$ model is studied using analytical and numerical methods. It is shown that the exact solutions for fermionic wave functions can be expressed in terms of the confluent Heun functions. The question of the existence of bound states for the fermion-soliton system is then investigated. General formulae describing fermion scattering are obtained, and a symmetry property for the partial phase shifts is derived. The amplitudes and cross-sections of the fermion-soliton scattering are obtained in an analytical form within the framework of the Born approximation, and the symmetry properties and asymptotic forms of the Born amplitudes are investigated. The dependences of the first few partial phase shifts on the fermion momentum are obtained by numerical methods, and some of their properties are investigated and discussed.

arXiv comment14 pages, 4 figures

References in corpus (14)

• Vortices, Instantons and Branes
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Non-Abelian String Junctions as Confined Monopoles
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Quantum Vortex Strings: A Review
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• Resurgence theory, ghost-instantons, and analytic continuation of path integrals
• Quantum Field Theory Applications of Heun Type Functions
• Fractionalized Non-Self-Dual Solutions in the CP(N-1) Model
• Clustering and decomposition for non BPS solutions of the ${\mathbb{CP}}^{N-1}$ models
• Scattering of fermionic isodoublets on the sine-Gordon kink
• Fermion scattering on topological solitons in the nonlinear $O(3)$ $\sigma$-model
• Scattering of fermions on a one-dimensional Q-ball

Cited by in corpus (1)

• Fermion-soliton scattering in a modified ${\mathbb{CP}}^1$ model