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Particular boundary condition ensures that a fermion in d=1+5, compactified on a finite disk, manifests d=1+3 as a massless spinor with a charge 1/2, mass protected and chirally coupled to the gauge field

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  • N. M. Borstnik
  • Holger Frits Bech Nielsen
The genuine Kaluza-Klein-like theories-with no fields in addition to gravity-have difficulties with the existence of massless spinors after the compactification of some space dimensions [E. Witten, Nucl. Phys. B 186 (1981) 412; E. Witten, Fermion quantum numbers in Kaluza-Klein theories, Princeton Technical Rep. PRINT-83-1056, October 1983]. We proposed in [N.S. Mankoc Borštnik, H.B. Nielsen, Phys. Lett. B 633 (2006) 771, hep-th/0509101; N.S. Mankoc Borštnik, H.B. Nielsen, hep-th/0311037] a boundary condition for spinors in (1+5) compactified on a flat disk that ensures masslessness of spinors (with all positive half integer charges) in d=(1+3) as well as their chiral coupling to the corresponding background gauge gravitational field. In this Letter we study the same toy model, proposing a boundary condition allowing a massless spinor of one handedness and only one charge (1/2) and infinitely many massive spinors of the same charge, allowing disc to be curved. We define the operator of momentum to be Hermitean on the vector space of spinor states-the solutions on a disc with the boundary.
Udgivelsesdato: May 22
OriginalsprogEngelsk
TidsskriftPhysics Letters B
Vol/bind663
Udgave nummer3
Sider (fra-til)265-269
ISSN0370-2693
DOI
StatusUdgivet - 2008

ID: 10455069