Abstract
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. Mankoč Borštnik, H.B. Nielsen, Phys. Lett. B 633 (2006) 771, hep-th/0509101; N.S. Mankoč 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
