Fermionic Zero Modes on Domain Walls

Abstract

We study fermionic zero modes in the domain wall background. The fermions have Dirac and left- and right-handed Majorana mass terms. The source of the Dirac mass term is the coupling to a scalar field $\Phi$. The source of the Majorana mass terms could also be the coupling to a scalar field $\Phi$ or a vacuum expectation value of some other field acquired in a phase transition well above the phase transition of the field $\Phi$. We derive the fermionic equations of motion and find the necessary and sufficient conditions for a zero mode to exist. We also find the solutions numerically. In the absence of the Majorana mass terms, the equations are solvable analytically. In the case of massless fermions a zero energy solution exists and we show that although this mode is not discretely normalizable it is Dirac delta function normalizable and should be viewed as part of a continuum spectrum rather than as an isolated zero mode.

6 pages, 3 figures, matches version published in PRD

References in corpus (2)

• The Dirac Sea Contribution To The Energy Of An Electroweak String
• Neutrino Masses and Mixing with General Mass Matrices

Cited by in corpus (32)

• Fermions on Thick Branes in the Background of Sine-Gordon Kinks
• Kink interactions in the (1+1)-dimensional ${\phi }^6$ model
• Localization and Mass Spectra of Fermions on Symmetric and Asymmetric Thick Branes
• Fermion Resonances on Multi-field Thick Branes
• Bulk Matters on Symmetric and Asymmetric de Sitter Thick Branes
• Localization of bulk matter fields, the hierarchy problem and corrections to Coulomb's law on a pure de Sitter thick braneworld
• Thick branes with a nonminimally coupled bulk-scalar field
• Can primordial magnetic fields seeded by electroweak strings cause an alignment of quasar axes on cosmological scales?
• Fermion localization on branes with generalized dynamics
• Fermion Resonances on a Thick Brane with a Piecewise Warp Factor
• Localization of Bulk Matters on a Thick Anti-de Sitter Brane
• Zero modes of fermions with general mass matrix
• Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
• Fermions on the kink revisited
• Bulk Matters on a GRS-Inspired Braneworld
• Network of Domain Walls on Soliton Stars
• Example of a self-consistent solution for a fermion on domain wall
• Neutrino Zero Modes and Stability of Electroweak Strings
• Fermion states on domain wall junctions and the flavor number
• Stable branches of a solution for a fermion on domain wall
• Coulomb's law corrections and fermion field localization in a tachyonic de Sitter thick braneworld
• Matter localization on brane-worlds generated by deformed defects
• Localized Fermions on Domain Walls and Extended Supersymmetric Quantum Mechanics
• Scattering of fermionic isodoublets on the sine-Gordon kink
• Scattering of Dirac and Majorana Fermions off Domain Walls
• Baryogenesis and CP-Violating Domain Walls in the Background of a Magnetic Field
• An introduction to kinks in ${\phi }^4$-theory
• Superconducting Cosmic Strings and One Dimensional Extended Supersymmetric Algebras
• Stretching the electron as far as it will go
• Localized Fermions on Superconducting Domain Walls and Extended Supersymmetry with non-trivial Topological Charges
• Zero modes and index theorems for non-Hermitian Dirac fermions
• Gravitational Wave Mountains: current-carrying domain walls