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arXiv · 1001.4679

"An effective two dimensionality" cases bring a new hope to the Kaluza-Klein[like] theories

D. Lukman·N. S. Mankoc Borstnik·H. B. Nielsen
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Abstract

One step towards realistic Kaluza-Klein[like] theories and a loop hole through the Witten's "no-go theorem" is presented for cases which we call an effective two dimensionality cases: In $d=2$ the equations of motion following from the action with the linear curvature leave spin connections and zweibeins undetermined. We present the case of a spinor in $d=(1+5)$ compactified on a formally infinite disc with the zweibein which makes a disc curved on an almost $S^2$ and with the spin connection field which allows on such a sphere only one massless normalizable spinor state of a particular charge, which couples the spinor chirally to the corresponding Kaluza-Klein gauge field. We assume no external gauge fields. The masslessness of a spinor is achieved by the choice of a spin connection field (which breaks parity), the zweibein and the normalizability condition for spinor states, which guarantee a discrete spectrum forming the complete basis. We discuss the meaning of the hole, which manifests the noncompactness of the space.

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D. Lukman, N. S. Mankoc Borstnik, H. B. Nielsen. 2011-05-20. "An effective two dimensionality" cases bring a new hope to the Kaluza-Klein[like] theories. https://doi.org/10.1088/1367-2630%2F13%2F10%2F103027

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