Fermionic Zero Modes on Domain Walls

Details Fermionic Zero Modes on Domain Walls Fermionic Zero Modes on Domain Walls

2000-07-28

arxiv.org/abs/hep-ph/0007343v2

Phys.Rev. D63 (2001) 025010

Physics

High Energy Physics

High Energy Physics - Phenomenology

6 pages, 3 figures, matches version published in PRD

Scientific paper

10.1103/PhysRevD.63.025010

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.

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