Generally-covariant and GL(n, R)-invariant model of field of linear frames interacting with complex scalar field

Generally-covariant and GL(n, R)-invariant theory of the field of linear frames interacting with the complex scalar field is presented. The invariance assumptions introduced into the theory result in a modified Born-Infeld-type nonlinearity of the model. A Lagrangian of the system is constructed, field equations are derived and two families of geometrically privileged solutions are found.