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No scale nonlinear σ model, hedgehog compactification, and the cosmological constant
Phys. Rev. D 50, 7538 – Published 15 December, 1994
DOI: https://doi.org/10.1103/PhysRevD.50.7538
Abstract
The ‘‘no scale nonlinear σ 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 σ 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 (Einstein’s 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.
References (3)
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- M. Gell Mann and B. Zwiebach, Nucl. Phys. B260, 569 (1985).
- Similar types of field configurations for a four index antisymmetric tensor field with components proportional to the four dimensional antisymmetric symbol have been studied before, also in the context of compactification mechanisms, by P. G. O. Freund and M. A. Rubin, Phys. Lett. 97B, 233 (1980), although the dynamics there is very different. Also in this case, just symmetry considerations dictate this form.