Dimensional reduction of spacrtime induced by nonlinear scalar dynamics and noncompact extra dimensions

Abstract

We discuss general aspects of dimensional reduction induced by nonlinear scalar dynamics, including the small fluctuation expansion of the action. The case of compact positively curved scalar manifolds described by symmetric spaces G/H is shown to be free of tachyonic instabilities; the spectrum consists of a graviton, a massless scalar and towers of massive spin-two, spin-one, and spin-zero fields. These towers are worked out explicitly for the case of a two-sphere. The case of noncompact negatively curved scalar manifolds inducing a noncompact nonhomogeneous space for the extra dimensions is studied in the particular example of SU(1,1)/U(1). The massless spectrum consists of a graviton and a scalar and suitable boundary conditions are seen to give a discrete spectrum, actual conservation of formally conserved quantities, and no problems of interpretation. We discuss positive energy.

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