Consistency of quantum cosmology for models of plane symmetry

The consistency of a D-dimensional quantum cosmology with (D-2)-dimensional plane symmetry is studied. For this class of models, it is shown that the effective Lagrangian in a minisuperspace for the D-dimensional Einstein Lagrangian has a form closely related to that for the bosonic string theory. In a restricted class of models, it has exactly the same form as that for the bosonic string theory, from which it is derived that the maximum number of space-time dimensions in the quantized model must be D=29.