'Effective two dimensionality' cases bring a new hope to the Kaluza-Klein(like) theories

TY - JOUR

T1 - 'Effective two dimensionality' cases bring a new hope to the Kaluza-Klein(like) theories

AU - Lukman, D.

AU - Borstink, N.S.

AU - Nielsen, Holger Frits Bech

PY - 2011/10/21

Y1 - 2011/10/21

N2 - One step towards realistic Kaluza-Klein(like) theories and a loophole through Witten's 'no-go theorem' is presented for cases that we call 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 that makes a disc curved on an almost S2 and with the spin connection field that 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 the left-right symmetry), 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 non-compactness of the space.

AB - One step towards realistic Kaluza-Klein(like) theories and a loophole through Witten's 'no-go theorem' is presented for cases that we call 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 that makes a disc curved on an almost S2 and with the spin connection field that 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 the left-right symmetry), 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 non-compactness of the space.

U2 - 10.1088/1367-2630/13/10/103027

DO - 10.1088/1367-2630/13/10/103027

M3 - Journal article

SN - 1367-2630

VL - 13

SP - 103027

JO - New Journal of Physics

JF - New Journal of Physics

ER -