Higher-dimensional geometric sigma models

Abstract

Geometric sigma models have been defined as geometric theories of metric excitations of a given background geometry, and then covariantized by identifying the coordinates of space-time with a set of scalar fields. By construction, these theories have the property of accommodating both the scalar matter of pure geometric origin and a ground state specified in advance. Using this fact, one can build a Kaluza-Klein geometric sigma model by specifying the background metric of the form M-4 x B-d, thus obtaining a theory free of the classical cosmological constant problem. Previously exploited ideas to use scalar fields in the form of a nonlinear sigma model coupled to gravity to trigger the compactification failed to give massless gauge fields after dimensional reduction. In this paper, sigma modified geometric a model is suggested, which reconciles the masslessness of the gauge fields with the zero value of the cosmological constant. [S0556-2821(99)03310-6].