Critical Strings from Noncritical Dimensions: A Framework for Mirrors of Rigid Vacuaa (original) (raw)

The rôle in string theory of manifolds of complex dimension D crit +2(Q−1) and positive first Chern class is described. In order to be useful for string theory the first Chern class of these spaces has to satisfy a certain relation. Because of this condition the cohomology groups of such manifolds show a specific structure. A group that is particularly important is described by (D crit +Q−1, Q−1)-forms because it is this group which contains the higher dimensional counterpart of the holomorphic (D crit , 0)-form that figures so prominently in Calabi-Yau manifolds. It is shown that the higher dimensional manifolds do not, in general, have a unique counterpart of this holomorphic form of rank D crit. It is also shown that these manifolds lead, in general, to a number of additional modes beyond the standard Calabi-Yau spectrum. This suggests that not only the dilaton but also the other massless string modes, such as the antisymmetric torsion field, might be relevant for a possible stringy interpretation.