No scale nonlinear model, hedgehog compactification, and the cosmological constant

The no scale nonlinear model is a six-dimensional (6D) Kaluza-Klein model containing an isovector scalar field whose dynamics has global SO(3) invariance and where a homogeneous nonlinear constraint is imposed. In contrast with the more standard nonlinear model, this constraint does not determine a particular scale for the strength of the isovector scalar field. In this model we study a mechanism for the compactification of two dimensions into a sphere by the presence of a hedgehog configuration of the isovector scalar field. Consistency with the gravitational (Einsteins for D=6) equations forces the strength of the hedgehog to be the Planck scale. The resulting 4D effective cosmological constant is zero if the 6D cosmological constant is also zero, without the need of fine-tuning parameters in the Lagrangian.